The forward broke a finger during the defeat by Celta Vigo in La Liga on Sunday, and when asked by AFP, Madrid said his absence from training was because of that injury, but also other discomfort he suffered in that match.
If Mbappe is unable to play against City on Wednesday, it would be a big blow for coach Xabi Alonso, with Spanish media reporting that a defeat would lead to his dismissal.
The 26-year-old striker has scored 25 goals in 21 matches across all competitions this season and has been Madrid's key player.