If Hassett becomes Fed chief, Hassett would leave his post as White House economic adviser.
"I want you to stay where you are, if you want to know the truth," Trump told Hassett at the White House on Friday.
In addition to Hassett, Kevin Warsh, a former member of the Fed, has been mentioned as a possible candidate to take over from Jerome Powell, whose term expires in May.
Trump has recently said he plans to announce his nominee for Fed chair within the next few weeks.
