President Trump said Tuesday that he has narrowed the search for the next Federal Reserve chairman down to five candidates, all of whom are viable nominees.

"Honestly, I like 'em all," Trump said of the five potential central bankers, speaking at a press conference with Greek Prime Minister Alexis Tsipras at the White House.

"I'll make a decision over the next very short period of time," Trump said.

One of the five candidates is current Chairwoman Janet Yellen, whose term expires at the end of January.

Trump reportedly also met with Stanford economist John Taylor, an advocate of rules-based monetary policy and the only other possibility with a Ph.D.

Jerome Powell, a current member of the Fed's Board of Governors who served in the George H.W. Bush Treasury and has a background in private equity, is also in consideration.

Trump is also weighing nominating Gary Cohn, his top economic adviser and the former president of Goldman Sachs.

The last name is Kevin Warsh, a former Fed governor appointed by former President George W. Bush.