The midfielder was forced to come off during Tuesday's defeat to Reading following a challenge by Dave Kitson.
Coppinger underwent an MRI scan on Thursday and while the full extent of the injury is still unknown, O'Driscoll is not ruling him out of Saturday's clash with Coventry.
"We haven't ruled him out but if you were a betting man you would say that he would miss Saturday," O'Driscoll told the club's official website.
"He left the ground on crutches but the next 24 hours saw it resolve quite a bit.
"We'll have to wait and see; everybody has got everything cross and if it is nothing serious, then he may miss out a couple of games and then we'll get him back - but we won't know until we get the results from the scan."