Trump is leaning toward appointing both current Fed Governor Jerome "Jay" Powell and Stanford economist John Taylor, the president told the "Sunday Morning Futures" program for a broadcast to be aired this weekend on FOX News Channel, according to FOX Business.
In a segment aired on the station Friday, Trump acknowledges that the market expects him to pick between Powell and Taylor. The FBN report indicates that Trump could nominate both, one for chair and the other for vice chair. Current Chair Janet Yellen's term expires in February while the most recent vice chair, Stanley Fischer, resigned effective a week ago.
"I have three people that I'm looking at and there are a couple others," he said. "I'd say I will make my decision very shortly."
At a Friday afternoon news conference, White House press secretary Sarah Huckabee Sanders acknowledged that both men are "under consideration" for the job but he "hasn't ruled out other options."
However, Trump indicated he also is still considering Yellen for reappointment.
"I also met with Janet Yellen, who I like a lot, I really like her a lot," he said.
Trump previously indicated he would make his decision by Nov. 3. Online prediction markets and multiple surveys, including one by CNBC, point to Powell as the likely next chair.
Other candidates include Gary Cohn, currently Trump's chief economic advisor, and former Fed Governor Kevin Warsh.
Read the full FOX Business report here.