Yellen's term ends in February. Trump is considering five candidates in total and is expected to announce his pick before he heads to Asia on Nov. 3.
The White House declined to give any more details on what the pair discussed.
Trump entered Thursday's meeting holding drastically different views of the Fed chair than he held before he took office.
Last month, Trump said he respected Yellen and cheered the stock market's success. Those comments were a far cry from Trump's remarks about the Fed chair when he was trying to win the White House.
In a September 2016 CNBC interview, Trump accused Yellen of trying to help then-President Barack Obama by maintaining near-zero interest rates. Trump said she should be "ashamed."
"Well, it's staying at zero because she's obviously political. She's doing what Obama wants her to do. And I know that's not supposed to be the way it is, but that's why it's low," Trump said. "Because as soon as they go up, your stock market's going to go way down, most likely or possibly ... I believe it's a false market because money is essentially free."
He suggested the Fed would raise interest rates once the new president took office, hurting the stock market.