Skuse was forced to sit out the weekend defeat at Burnley after suffering a bad reaction to playing twice in the space of four days against Derby and Sheffield Wednesday over Easter.
City head coach Sean O'Driscoll hopes to have the 27-year-old available for Saturday's visit of Bolton and next week's matches against Birmingham and Hull.
"Cole has had this knee cartilage problem for quite a while now and playing two games in four days caused it to flair up," O'Driscoll told the Bristol Evening Post.
"Rather than risk him at Burnley, we felt he would be better off resting. He will probably have an injection in it so that he can try and get back by the end of the week."
Skuse first injured his knee during the 2-0 home win over Watford on January 29 and missed the next six games.
The Bristolian returned against Brighton on March 5 and then featured against Derby and Sheffield Wednesday before suffering a recurrence of the problem on April 1 against the Owls.