Osman has been out since limping off at half-time during the Merseyside derby victory over Liverpool on October 17.
It was initially thought the 29-year-old could be back in action within six weeks of that date but an operation has since become necessary.
Manager David Moyes said: "He had an operation on Monday morning to take away a piece of floating bone from his ankle.
"We expected him to be out for four to six weeks, but we think he probably be out for another six weeks now.
"He seems fine. Hopefully this will help his ankle."
Moyes appears to have all but ruled out a return for Jack Rodwell in Saturday's Premier League clash at Blackpool.
The 19-year-old midfielder has made a quicker than expected recovery from an ankle injury and was an unused substitute against Stoke last week.
He followed that up with an appearance for the reserves against Blackpool in midweek but he is unlikely to get further than the bench at Bloomfield Road on Saturday.
Moyes said: "I think he is close but I don't think he is quite ready yet.
"We may continue to include him on the bench but I don't think he is quite fully confident in his ankle yet.
"He played 50 minutes in the reserves and more than likely he will be included again tomorrow.
"But do I think he is ready to start? No, I don't.
"He is back ahead of schedule but it is likely to be another couple of weeks."