The England international was hurt during Wednesday's 1-0 defeat by Cluj in the UEFA Champions League, limping off just before half-time.
Red Devils manager Sir Alex Ferguson hoped the prognosis was good for the 23-year-old, but admitted on Friday that further investigation was needed, saying: "Tom is having a scan. It is a calf. We shall see."
Ferguson also claims Shinji Kagawa and Nemanja Vidic are unlikely to be available for the clash with City at the Etihad Stadium, with the duo still working their way back to full fitness following knee injuries.
"I thought Kagawa may have a chance but he is still a bit short. He won't be available until Sunderland next week," Ferguson added.
"Nemanja Vidic is certainly doing well in training. It is just his own confidence to play. He will be ready for Sunderland."
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar