The left-back is suffering from a back complaint and is a doubt for the crucial first leg game against Leonardo Jardim’s side, with manager Pep Guardiola admitting earlier in the day that he could miss out.
Vincent Kompany also failed to train, as did long-term absentees Ilkay Gundogan and Gabriel Jesus.
Addressing the media on Monday, Guardiola said: “Clichy had a problem in the back, it is much better. [But] I don’t know if he will be ready for tomorrow.
“He [Kompany] is not ready for tomorrow. It will not be longer, hopefully. For the Huddersfield game he will be ready but not tomorrow.”
The rest of the squad are fit and available to play against the Ligue 1 leaders, with youngsters Aleix Garcia, Tosin Adarabioyo, Cameron Humphreys and Isaac Buckley-Ricketts involved in the session.
Monaco boss Jardim confirmed the 21 players who have travelled to Manchester are all fit and in contention to play on Tuesday.