But the 27-year-old came on as a second-half substitute in last weekend's opening win at Swansea, setting up goals for Robin van Persie and Danny Welbeck.
"Wayne has recovered and has a good chance of starting," Moyes said.
Earlier Friday, Moyes reaffirmed United's stance that Rooney will not be sold to Chelsea.
Mourinho has suggested he will make a third bid for the England international following Monday's game at Old Trafford.
But when asked if there had been anything further on Rooney's future, Moyes said: "We have said it haven't we? It is still the same message."