If confirmed by the Senate, Milley would succeed Marine Gen. Joseph Dunford to be chairman of the Joint Chiefs of Staff.
Milley is a veteran of the Iraq and Afghanistan wars and has served as the Army's top officer since August 2015.
Speaking to reporters on Friday, Trump hinted an announcement related to the Joint Chiefs of Staff was forthcoming as he unveiled other picks - William Barr for attorney general and Heather Nauert for United Nations ambassador.
The president reportedly plans to make the announcement at Saturday's annual Army-Navy football game.More news: José Mourinho sees no place for Fred until Manchester United tighten up
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President Donald Trump said he'll be making an announcement on Saturday concerning the Joint Chiefs of Staff. "I can give you a little hint: It will have to do with the joint chiefs of staff and succession". Typically, the successor to the chairman would not be selected until next year, given that Dunford is due to serve until October 1, 2019.
Dunford was picked as chairman of the Joint Chiefs in 2015 by former President Barack Obama.
Two defense officials tell CNN that Milley and Trump will be together on the Army side of the field during tomorrow's game and then Trump is expected to visit the Navy side during the second half of the game.
Although Kelly was not serving as Trump's chief of staff during the time he fired former FBI Director James Comey, Mueller's team nonetheless wanted him to answer some questions about what he remembered about key events surrounding the firing.