Goal.com exclusively revealed on Tuesday that the England international faces a race to be ready in time for the crunch tie with the Spanish giants.
The defender injured his ankle in the 2-1 win over Reading in the FA Cup on Monday night, leaving Old Trafford on crutches after the clash.
The Scot admitted at the time that he could miss their Premier League game with QPR on Saturday, and has now stated he may not recover in time to face Jose Mourinho's side on March 5.
He told reporters: "Phil Jones is the one we're concerned about for the Real Madrid game. We're working hard on it and I'd say he has an outside chance - no more than that.
"We'll have to wait and see if he's fit for the second leg. It's two weeks away. A lot can happen. He's an outside chance, that's all. Other than that, everybody's fit."
Aside from Jones' problem the Red Devils manager should have a virtually full-strength squad to pick from for the league match on Saturday, although Wayne Rooney has also been ruled out of the QPR clash.
"We have a problem picking teams at the moment but that's where we want to be," he continued. "QPR are fighting for survival and we know it's going to be a hard game.
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"That's what we need - we need to make sure we do our job right. The fact is, City will drop points too. Coming into the run-in we expect to drop a few points but so will they.
"To be honest, it's always a hard run-in in the Premier League. With the right attitude and the right players we have a chance."
United will be without chief executive David Gill come the end of the season, the 55-year-old announcing that he will step down in June, although he will remain a director on the board.
However, Sir Alex believes Gill's decision will not harm the club, suggesting they will be able to keep some continuity and follow on from his work.
"There's a good stability here," he added. "The foundations David's laid down, it's easy to carry on from that. There's a template we can follow and I think that's what Ed [Woodward] will do.
"The job is to support the manager and staff so we can maintain the success we have. I don't think that should change that much."