Mueller has assembled a high-powered team of top investigators and leading experts, including seasoned attorneys who've represented major American companies in court and who have worked on cases ranging from Watergate to the Enron fraud scandal.
Among them are James Quarles and Jeannie Rhee, both of whom Mueller brought over from his old firm,
WilmerHale. He's also hired Andrew Weissmann, who led the Enron investigation.
"That is a great, great team of complete professionals, so let's let him do his job," former independent counsel Kenneth Starr, who investigated President Bill Clinton in the 1990s, told ABC News.
While only five attorneys have been identified, concerns have come up over the political leanings
of Quarles, Rhee and Weissmann. They have donated overwhelmingly to Democrats
, totaling more than $53,000 since 1988, according to a CNN analysis of Federal Election Commission records.
The special counsel's investigators are looking into questions of Russian interference in last year's election, and plan to speak to senior intelligence officials, a source familiar with the matter told CNN.
Mueller is also investigating whether President Donald Trump attempted to obstruct justice, The Washington Post
The Post reported
that the interviews represent a widening of the probe to include looking into whether the President obstructed justice in suggesting to his former FBI Director James Comey that Comey drop the investigation into Michael Flynn, Trump's former national security adviser, as well as for his firing of Comey.
Mueller's investigators have asked for information and will talk to Director of National Intelligence Dan Coats and National Security Agency Director Adm. Mike Rogers, according to a source, who said they have also sought information from recently retired NSA Deputy Director Richard Ledgett. Coats and Rogers have testified that they were not pressured by the Trump administration.
The interviews are some of the first indications of the efforts of Mueller's newly assembled team.
Ultimately, it would be up to Mueller to decide whether there is enough evidence to recommend pursuing charges on any part of the investigation.
Law enforcement sources tell CNN that the special counsel is gathering information and considering whether there is evidence to launch a full-scale obstruction investigation.
Trump, however, referred to the Post's reporting as a "phony" story in a tweet Thursday.
"They made up a phony collusion with the Russians story, found zero proof, so now they go for obstruction of justice on the phony story. Nice," the President tweeted
In another tweet, Trump called it "the single greatest WITCH HUNT in American political history -- led by some very bad and conflicted people!"
A spokesman for the office of the special counsel declined to comment, and so did a representative for the director of National Intelligence. In a statement, the National Security Agency said it "will fully cooperate with the special counsel," but declined to comment further.
Mark Corallo, a spokesman for Trump's outside attorney, Marc Kasowitz, slammed the Post's reporting. "The FBI leak of information regarding the President is outrageous, inexcusable and illegal," he said.
Fire special counsel?
As Mueller assembles his investigative team, statements by Trump's friend Christopher Ruddy this week set off new questions.
Ruddy, who had been at the White House on Monday, told PBS that Trump is considering terminating the special counsel.
"I think he's weighing that option," he said of Trump.
But a source close to the President told CNN's Jim Acosta that Trump has been advised to avoid such a dramatic move.