Antonio Valencia could be fit in time to face Tottenham at White Hart Lane on Sunday 4 March.
The classy winger suffered a hamstring strain after coming on as a substitute in the first leg victory against Ajax in the Europa League and was expected to be out for around a month.
However, Sir Alex is hopeful that the right-sided midfielder will be back in contention for a starting spot against third-placed Spurs.
"The availability of Ashley Young and Nani as natural wide players considerably strengthens our attacking options," the boss wrote in his column for United Review, the official matchday programme. "And I am sure our strikers are pleased to see them.
"They will be sorry to see Antonio Valencia injured again because he too provides great service from out on his wing, but it's not a particularly serious injury and he should be back in a week or so."
Valencia will miss Sunday's trip to East Anglia to face Norwich City as the champions look to keep the pressure on Manchester City at the top of the table.