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.
Since Trump's comments, the central bank has hiked its target federal funds rate range three separate times, by a total of 0.75 percentage point. Major stock indexes have kept climbing to record highs, a fact that President Trump cheers often.
Trump spoke much more highly of Yellen — and the stock market — in September.
"I like her and I respect her, but I haven't made that decision yet" on who will lead the Fed, he told The Wall Street Journal.
He added that "the stock market is doing very well."
Aside from Yellen, Trump is considering his chief economic advisor Gary Cohn, former Fed Governor Kevin Warsh, Fed Governor Jerome Powell and Stanford University economist John Taylor for the post.
Powell has the best chances of becoming the next Fed chair at 44 percent, according to the PredictIt platform. Yellen has the second-highest chance of the candidates at 24 percent, PredictIt says.