Jonny Evans could recover from a minor groin strain sustained in Braga to face Aston Villa on Saturday, but Nani is set to be sidelined for 10 days.
The winger was substituted in United's midweek Champions League victory after complaining of a tight hamstring and will need a short period of rest before he can take to the field again.
"We're hoping Evans will be okay for Saturday," Sir Alex told media at his pre-match press conference on Friday morning.
"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."
Should Jonny Evans fail his fitness test, the manager will ask Chris Smalling to step into the breach.
Smalling played his first football since early May in Braga, having been sidelined after sustaining a broken foot during pre-season training.
"We're monitoring the situation with Jonny," Sir Alex confirmed. "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."
The Reds travel to Villa Park on Saturday as league leaders and with a formidable record at the ground. United have lost there just twice in 20 previous Premier League games.
But after seeeing Tottenham win at Old Trafford this season for the first time since 1989, Sir Alex