Speaking to MUTV after Saturday's 1-0 win at Carrow Road, the boss said: "I am hopeful and I think he will be fit for New Year's Day. I just need to wait and see.
"He has got the same injury that kept him out at Stoke. It is an adductor injury to his groin, it is not serious but ideally we could have given him two or three weeks to recover completely. But he has been so influential for the team and we want to get him back playing."
Rooney's sumptuous half-volley in the Boxing Day victory over Hull City was his 11th strike of the season so far in all competitions and notably his 150th goal in the Barclays Premier League for United.