Trump did not specify who is his leading chair candidate and said an announcement would be made in "January sometime"
Trump made the comments during a national address touting his economic and national security accomplishments in the first year of his second term in office
Trump previously signalled that he already made up his mind, saying Monday he had a "a pretty good idea" of who to nominate
The president on Sunday told reporters he knew who he would nominate, without offering further details
The team chosen by Trump has been reviewing several contenders, including a former Fed president and a longtime economic consultant
Potential arrangement was discussed between Trump and Warsh, a former investment banker who served on the Federal Reserve Board, at Trump's Mar-a-Lago retreat
Professor at the University of Chicago's Booth School of Business, Diamond received the prize along with Philip Dybvig and former Fed chair Ben Bernanke
The White House is cognisant of pressure from both moderates and progressives within the Democratic Party about the choice
Trump teased the announcement Friday by tweeting out a video promoting the event to his 41 million Twitter followers
Trump has said he has been considering Powell, as well as Stanford University economist John Taylor, for the post