Trump will make the announcement at this weekend's Army-Navy football game, the Washington Post reported, citing individuals familiar with the plan.
Milley is a four-star general and Chief of Staff of the Army since 2015.
The report comes amid other appointments, declared by Donald Trump: the US president said he would nominate spokeswoman for the Department of State, Heather Nauert as the 30th US envoy to the United Nations, while former Attorney General William Barr would head the Justice Department.