(CNN) —  

President Donald Trump is firming up his shortlist of contenders for the next Supreme Court nominee as aides say he is pushing to play up the drama around his search and is increasingly intrigued by the prospect of selecting the first truly conservative female justice.

Trump told reporters on Monday that he had interviewed four candidates to replace retiring Justice Anthony Kennedy earlier that morning, signaling an aggressive push toward picking a nominee before his self-imposed deadline of July 9.

Later, people familiar with the matter told CNN the potential nominees who were interviewed were Amy Coney Barrett, Brett Kavanaugh, Raymond Kethledge and Amul Thapar.

A source close to the process said the President’s talks Monday morning with the Supreme Court contenders were related to the burdensome technical process each must navigate if he or she is to accept the nomination, including a lengthy Senate questionnaire and thorough FBI background check.

Several of Trump’s top candidates have already filled out the paperwork required to start the confirmation process – either because they made it onto the President’s shortlist the last time there was a Supreme Court vacancy or because Trump nominated them to appeals court posts relatively recently. One judge on the shortlist has not, the source close to the process said, and that judge, Kavanaugh, will likely be asked to start the questionnaire soon in case Trump decides to nominate him next week.

People familiar with the search said Trump has repeatedly told advisers that he likes the idea of making the choice of a female justice in a climate where women on the Democratic side of the political aisle are playing such a pivotal role.

In conversations with advisers and associates in recent days, the President has spent considerable time openly ruminating on the advantages of nominating a woman to fill Kennedy’s seat. He believes such a choice could also be more palatable with critical Republicans senators like Maine’s Susan Collins and Alaska’s Lisa Murkowski, according to three people familiar with the search.

“Can you imagine?” the President said with a smile during a recent conversation about the prospect of selecting a woman for the pivotal spot on the court.

But others in Trump’s orbit have pushed for what they consider a safer and more traditionally conservative pick to replace a justice who had frustrated ideological hardliners on both sides of the aisle during his decades on the bench. Kavanaugh, a judge on the United States Court of Appeals for the District of Columbia Circuit, is seen as one of the candidates who most closely fits the criteria used to select Justice Neil Gorsuch, Trump’s first Supreme Court nominee.

Another leading contender is Barrett, a federal judge who is receiving considerable praise from conservative leaders, including today on Twitter from former House Speaker Newt Gingrich.

“Her clarity and intellectual strength in the Senate hearings for her current judgeship showed an intellect and a depth of thought that would be powerful on the Supreme Court,” Gingrich said.

Those kind words are part of an outside campaign to gain Trump’s attention. Barrett is one – but not the only – female candidate who is viewed by conservatives as highly qualified and desirable for the post. The source close to the process noted Barrett is one of the five top contenders who has already filled out the lengthy Senate questionnaire due to her recent confirmation as a judge on the Court of Appeals for the Seventh Circuit.

While it’s far too early to know whether Trump will choose a woman when he makes his announcement next week, people familiar with the process say he wants the option of at least one or two – or more – female contenders to consider.

In a weekend conversation with at least one adviser, the President was fondly recalling how he enjoyed the historic moment of choosing the first woman to lead the CIA when he picked Gina Haspel earlier this year. Choosing a conservative woman to fill Kennedy’s seat, he has told people, would be magnified considerably more in a midterm election year already dubbed the “year of the woman.”

Sandra Day O’Connor is the only female justice to serve on the court who was appointed by a Republican president, but conservative activists hardly viewed her as a champion for their core beliefs.

Trump considers the appointment of the staunchly conservative Gorsuch one of the crowning achievements of his presidency to date.

Kavanaugh has been in the sights of Trump’s team for more than a year. Two sources said he was discussed internally as a potential pick to replace Kennedy, in anticipation of his potential retirement, as far back as last spring, when the previous Supreme Court term was coming to an end. Kavanaugh, a former Kennedy clerk, has a larger body of written opinions than Barrett, and one source said the volume of his writings could ensure he is a better-vetted choice ideologically than Barrett. Another source, however, noted there are “proxies” for judicial opinions that the White House is considering in her case, including her academic writings.

Kethledge, another former Kennedy clerk, is also viewed as a leading contender, people familiar with the search said. The ties both Kavanaugh and Kethledge have to the man one of them could replace – Kennedy – would make for a historic tribute to the retiring justice, as the confirmation of either would put a second former Kennedy clerk on the bench alongside Gorsuch and cement Kennedy’s legacy for decades to come.

Kethledge made it through the “intermediate screening process” when Trump’s team was sifting through candidates for the nomination that ultimately went to Gorsuch, the source close to the process said, and so Kethledge is among the five with completed paperwork – a factor that would allow the White House to move quickly if Trump were to select him. Kethledge did not make it far enough in the process to get an interview with Trump last year.

Two other prospects – Thapar, who Trump nominated to the US Court of Appeals for the Sixth Circuit last year, and Thomas Hardiman, who Trump formally interviewed just before selecting Gorsuch – are also in contention, although the source said Hardiman is further from the top of the list because there are “others who are capturing everyone’s attention a little bit more right now” inside the White House. Both Hardiman and Thapar have completed paperwork for Trump’s team to examine, the source noted.

A thorough review process

Two sources said White House counsel Don McGahn and his team had been working on the Supreme Court search for months before Kennedy announced his retirement, knowing that his departure at the end of the term was a possibility. That process involved combing through candidates’ most recent opinions for evidence of wavering from the conservatism that placed them on Trump’s list of 25 contenders in the first place, one source close to the process said.

The sources said social conservatism was not a major part of the criteria used to select Gorsuch and is not a major factor in the latest round of deliberations. Instead, Trump’s team of aides and advisers are more concerned with how candidates have decided on cases involving administrative law, where the power of government is questioned by the courts.

The President is more concerned with a candidate’s resume, ability to resist political winds and dedication to the Constitution, the source close to the process said. Trump will not ask his potential nominees about specific opinions.

And Trump’s personal chemistry with the eventual nominee is “very important,” the source noted.

“He wants to judge a person’s leadership, strength, integrity, fairness. Are they articulate? Are they forceful in their presentation? Do they demonstrate that they care very deeply about the Constitution and the rule of law? Do they understand the proper role of a judge? Are they able to articulate all of those things in a way that will inspire?” the source said of what Trump will look for during the 40-to-50-minute interviews he will conduct with each candidate. “He wants to know who a person is, who are you, what distinguishes you, what are the key aspects of your life? An interview for the US Supreme Court is really, in a way, like every other interview.”

McGahn in particular has pushed to focus the selection process on how judges have spoken or written about administrative law, people familiar with the process have said.

Putting on a show

As he did when selecting Gorsuch in the early weeks of his administration, Trump has sought to play up the drama of the selection process. The President announced the nomination of Gorsuch during a prime-time event from the East Room, and the White House did not formally reveal his name until he walked on stage alongside Trump.

The President is already busy building anticipation for the announcement, which aides say is expected to be made during prime-time next Monday. Aides say the goal is to reveal virtually no specific information about who Trump is holding face-to-face interviews with this week, but for him to keep talking in general about the selection to keep the conversation alive this week.

He did just that on Monday ahead of talks with the Dutch prime minister in the Oval Office.

“During the morning I interviewed and met with four potential Justices of our great Supreme Court. They are outstanding people. They are really incredible people in so many different ways, academically and every other way,” Trump said without revealing their names or any identifying features.

“I’ll be meeting with two or three more and we’ll make a decision on the United States Supreme Court, the new Justice, that’ll be made over the next few days and we’ll be announcing it on Monday and I look forward to that,” Trump said. “I think the person that is chosen will be outstanding.”

In conversations over the past week, Trump has marveled at the chance he has to reshape the court. He’s noted with pride that his predecessor Barack Obama named two justices to the Supreme Court over the course of his eight years in office, while Trump is likely to fill two seats within his first two years.

Aides took measures to conceal Gorsuch’s nomination until the last moment. He was spirited away from his home in Colorado down rural country roads by members of the White House counsel’s office before flying aboard a military aircraft to Washington. He stayed in his hotel room until the last minute to avoid detection.

The White House is taking pains this time around as well to prevent the identity of Trump’s pick from leaking before the President unveils his nominee next week. One former senior White House official said, in the days leading up to Gorsuch’s nomination, that involved allowing as few people as possible into the loop and minimizing “who knew what” among the other aides tasked with working on the search.

Trump has indicated he wants to follow a similar playbook because he wants to maintain public interest in his selection, which he believes will help him politically.