Trump officially starts the race

Trump told the WSJ that Yellen remains a contender to lead the Fed and that Gary Cohn is also up for consideration.

Trump also said "two or three others" are under consideration.

On Cohn, he said this:

"He doesn't know this, but yes he is," he said, when asked if Mr. Cohn, who was present during the interview, was a candidate for the job. "I actually think he likes what he's doing right now."

"I've known Gary for a long time, but I've gained great respect for Gary working with him, so Gary certainly would be in the mix," Trump said.

Here's what he said on Yellen:

"I like her; I like her demeanor. I think she's done a good job," he said. "I'd like to see rates stay low. She's historically been a low-interest-rate person."

More: Gary Cohn has an embarrassing misunderstanding of the Swiss franc