The 23-year-old limped out of United's 1-0 Champions League defeat to Cluj on Wednesday, leaving him doubtful for Sunday's eagerly-anticipated clash with Manchester City.
Manager Sir Alex Ferguson said: "Tom Cleverley is having a scan today (Friday). It is a calf. We shall see."
Ferguson also revealed that Shinji Kagawa and Nemanja Vidic, who have both suffered knee injuries, are struggling to be fit in time for the derby match at the Etihad Stadium.
He said: "I thought Kagawa may have a chance but he is still a bit short. He won't be available until Sunderland next week.
"Nemanja Vidic is certainly doing well in training. It is just his own confidence to play. He will be ready for Sunderland."
United's defence has come under scrutiny following the 4-3 victory at Reading last week.
And Ferguson admitted set piece defending has been worked on at the training ground since.
He said: "Manchester City will have expected us to work on it (defending set pieces). I am sure they have (attacking them)."