The 31-year-old missed Tuesday's goalless draw with Arsenal with a groin problem.
Moyes said that the midfielder is making progress, but only has an "outside chance" of recovering in time.
"Leon's getting better," the Scot told reporters. "I don't know if [the game] will come too quick for him.
"He'll have an outside chance so we'll need to see how he is."
Osman has scored five goals this season.