The 38-year-old midfielder has been struggling with a knee problem that forced him to sit out the side's trip to the Bernabeu in midweek, with the initial hope of involvement against Reading in the FA Cup fifth round on Monday.
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However, Sir Alex revealed on Friday that the veteran is sidelined for "another couple of weeks".
"It is a knee injury, which has been bothering him a bit," Sir Alex told reporters.
"We have tried another treatment during the week. He will probably be back in another couple of weeks."
On a more positive note, Sir Alex confirmed that the squad came away from Wednesday’s 1-1 draw with Real Madrid unscathed, but he will be making changes for the visit of Reading in three days’ time.
"I will make some [changes]," he added.
"We want to get to the quarter-finals and we do expect to qualify."
Much of the talk after the Bernabeu clash was that of David De Gea’s performance, the oft-criticised goalkeeper thwarting Madrid time and time again.
Sir Alex acknowledged the 22-year-old’s continual progression at Old Trafford, but admitted mistakes are to be expected after thrusting the youngster into the limelight at such an early age.
He continued: "He is maturing."
"Very few goalkeepers go into the first team at 20. Gianluigi Buffon and Petr Cech are two examples of those who did but it is not always the case.
"Peter Schmeichel didn't join us until he was 27, and he gave us eight great years."