The England striker has missed the last two matches with a groin injury, while the Brazilian full-back was withdrawn in the first half against Sunderland last Saturday
As reported by Goal.com on Wednesday, the United boss is willing to risk the England striker despite having missed the matches against Sunderland and Chelsea over Easter.
Nemanja Vidic and Jonny Evans, however, are yet to take part in preparations for the match at Old Trafford after also sustaining knocks on Wearside.
"Wayne and Rafa have started training this morning, which is good news," Sir Alex told reporters on Thursday.
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The 71-year-old also responded to criticism that has come United's way since they were eliminated from the FA Cup by Chelsea on Monday and believes that, as long as his side win the league, it will not be a disappointing season.
"The way we've approached things is the correct way and that's to win the next game," he added.
"Hopefully, it takes us to winning the league. It doesn't matter what people say outside of the club, it's about what we think inside the club. We're always looking to do our best. It's been a good season for us.
"It's a derby game with a difference from a few years ago. 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."
Sir Alex also praised his players for their league form, which has handed them a 15-point gap over City at the top of the table.
He beamed: "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."