The 29-year-old has featured 249 times in a decade at the west London club, in which time he has won two Premier Leagues, four FA Cups, a Champions League and the Europa League.
Mourinho signed Mikel during his first stint as manager at Chelsea from 2004 through 2007, and then used him frequently during his return in 2013, which ended in dismissal in December 2015.
Manchester United is sixth in the Premier League table, 11 points short of leaders Chelsea.
