Departing the White House for his golf club in New Jersey, Trump said he'd decide in two or three weeks.
Among those who met with Trump were Kevin Warsh, a leading choice to lead the Federal Reserve, a sign he is scaling up his involvement in the search
for one of the nation's most critical posts.
He also met with Jerome Powell, a current Federal Reserve governor, to discuss the post.
A person familiar with the meetings confirmed Trump met with both men, but offered no other details about the sessions. The meetings come as Trump weighs his options ahead of an expected October nomination.
It wasn't immediately clear who Trump's two additional meetings were with.
Considered by some the second-most important job in the country, Trump's Fed chair decision could have wide-reaching effects on the economy. The Federal Reserve operates outside the scope of the administration, meaning the person Trump chooses for the job will not be beholden to Trump's directions.
Warsh, who has previously served as a Federal Reserve governor, has emerged as a leading candidate. He has a personal connection to Trump as a son-in-law of Ron Lauder, a close friend of Trump's who has sung Warsh's praises to the President.
Powell served in President George W. Bush's Treasury Department and, before that, as a partner at the Carlyle Group, a private equity firm. He has held a Fed seat since 2012.
Until this month, Trump had not engaged on the search for a Fed chair directly. A small team led by Treasury Secretary Steve Mnuchin has worked to put together options for Trump as he approaches the time when a decision has typically been made by a president in their first term.
Both Presidents Bush and Barack Obama offered nominations for the federal reserve between the months of August and October. Yellen's term expires at the end of January, and a potential replacement would require Senate confirmation.
Trump has not ruled out renominating Yellen, who he lambasted on the campaign trail last year but since has praised. Yellen met Trump shortly after he took office, but she has not met with him since then, she said last week at a news conference.
Most presidents renominate the sitting Fed chair upon taking office, though Trump has shown little adherence to presidential custom. Officials familiar with the process said it was too early to place odds on Trump's choice, since his direct involvement in the search has only recently begun.
Earlier this year, National Economic Council head Gary Cohn was considered a favorite for the post, but his standing plummeted after he distanced himself
from Trump's equivocal remarks about white supremacist violence in Virginia.
Since then, Cohn and Trump do appear to have repaired their relationship to some degree, according to people familiar with the two men. Cohn continues to be the White House driver on a tax reform effort and has been highly visible this week in interviews and press briefings to deliver the President's message.
On Thursday, Cohn stumbled somewhat in answering questions about the tax reform effort, including misstating the average American income and suggesting a kitchen could be renovated for $1,000. But Trump nonetheless regards Cohn as largely irreplaceable on the effort.
People who have spoken to Cohn say-- at this point -- he does not believe he is in the running to become Fed chairman, but all parties insist the process is nowhere near its final stages, and Cohn could come back into play.
Other potential candidates include John Taylor, an economics professor at Stanford who served in both Bush administrations; Glenn Hubbard, the dean of the Columbia Business School who has been floated as a potential Republican Fed nominee for years; and John Allison, a former banking executive.