The Serbian suffered the setback in September, just a month after recovering from a cruciate ligament problem, with the Red Devils' manager stating at the time that he did not expect his defender to return until after Christmas.
However, the 31-year-old has made good progress in his recovery, with Sir Alex confirming the centre-half is back in training, while hinting he could make first-team return as early as next week.
He told reporters: "Vidic has started training which is good news. I wouldn't be averse to playing him on Wednesday [against Cluj]."
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Sir Alex also noted that another wide man, Antonio Valencia, is likely to be out of the Premier League game with Reading on Saturday, but said Nick Powell, Paul Scholes and Ryan Giggs could all feature.
"Nani and Valencia are still out," the 70-year-old added. "Nani could be four-five weeks. It's a hamstring problem - you have to take your time with them.
"Antonio should be fit for next week. He's got a hip injury which is painful but is getting better.
"Nick Powell has had a virus but should be okay for tomorrow.
"Scholes is back from suspension. Giggs has had a slight hamstring strain but should be okay for tomorrow. Everyone else is fine."