The Portuguese felt the strain following his side's win over Braga on Wednesday, whilst team-mate Jonny Evans is also battling a groin injury picked up in that fixture.
But Sir Alex believes the Northern Irishman could recover in time to face Aston Villa on Saturday, though that will not be the case for the enigmatic winger.
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"We're hoping Evans will be okay for Saturday," Sir Alex told reporters at his pre-match press conference.
"He's a doubt, although not a serious one. Nani is out with a tight hamstring and that will be around 10 days but he should be okay. It's not torn, just tight."
Chris Smalling could feature again should Evans fail to make the trip to Villa Park, but Sir Alex admitted he is reluctant to use the young centre-back again so soon after his return from a long lay-off.
He added: "We're monitoring the situation with Jonny, If he doesn't make it then Chris will have to play.
"It's asking a lot for him to play Wednesday and then Saturday [when he's just come back].
"The great thing is that he's back and there are no issues with him at all. He did very well on Wednesday - we were pleased with that."