Wayne Rooney and Rafael are back in training ahead of the derby clash with Manchester City.
The pair missed the FA Cup exit at the hands of Chelsea and there are still question marks over the availability of centre-backs Jonny Evans and Nemanja Vidic, who also sat out the Stamford Bridge clash.
The fact that the Old Trafford showdown with second-placed City is on Monday night at least gives United plenty of time to work on the fitness of those who are carrying injuries.
"Wayne and Rafa have started training this morning," stated Sir Alex. "Which is good news.
"Hopefully, they will be fine by Monday. Jonny Evans and Nemanja Vidic are not there yet but, hopefully, they will start training maybe tomorrow or Saturday morning. We have a little bit of time on our hands to get most of the troops ready for the game."
City will be determined to stop the Reds from taking another massive step towards regaining the Barclays Premier League crown in what promises to be an exciting encounter.
"It's a derby game with a difference from a few years ago," explained the boss at his press conference. "We have to get used to playing Manchester City in big games and that's the case again.
"The important thing is to win Monday's game. It'll be a big game for City. They'll want to come and derail us for a spell. We're at home and our consistency is there for all to see. I expect us to perform really well on Monday.
"We have to congratulate our players on their consistency - to win 25 out of 30 games is a record and should be applauded. It's fantastic. But we've still got to win the title. We have eight games left and that's 24 points to play for.
"The way we've approached things is the correct way and that's to win the next game. Hopefully, it takes you to winning the league and then we talk about what the season has been like. It doesn't matter what people say outside of the club, it's about what we think inside the club about what we've achieved.