Wayne Rooney and Javier Hernandez will both return from injury for Saturday's Barclays Premier League visit of Norwich City.
Sir Alex delivered the good news at his Friday press conference at Carrington, where he also indicated Jonny Evans could be fit to take his place in the back four.
Rooney, who has scored nine goals in his first five league games this term, hasn't played since the 3-1 win over Chelsea on 18 September, while Hernandez came off with a dead leg early in last weekend's draw against Stoke.
The Norwich game comes too soon for Nemanja Vidic, Tom Cleverley and Chris Smalling, who should be back for the trip to Liverpool on 15 October.
"Wayne and Hernandez are fit for tomorrow," Sir Alex said. "They trained very well yesterday, which is pleasing.
"We'll hopefully have Jonny Evans back too. At the moment we're making too many changes in the back four so hopefully his return will help us with the defensive part.
"Vidic, Cleverley and Smalling should be ready after the internationals and available for Liverpool."
After United's 20-game winning run at Old Trafford in all competitions came to an end with the surprise Champions League draw with Basel on Tuesday, Sir Alex will be keen to avoid a repeat this weekend, when the Reds can still set a new club record of 19 straight home league wins.
"People will say our performance was careless [against Basel] and that we underestimated our opponents," the Reds boss added. "I think there's an element of truth in that and we have to do better defensively."
Carlos Tevez's alleged refusal to play for Manchester City has dominated the back pages this week, with the media garnering reaction from anyone and everyone in the football world.
Sir Alex did not want to dwell on the subject but said of City's boss: "I think Roberto Mancini has come out and shown his strength of character and strength as a manager which is important in today's management.