The 21-year-old hurt an ankle during Monday's FA Cup victory over Reading and has already been ruled out of this weekend's Premier League game at Queens Park Rangers, along with Wayne Rooney who has a sinus problem.
Manager Sir Alex Ferguson says the defender-cum-midfielder is undergoing intense treatment but accepts he may not be ready for the second leg of their last-16 showdown with Real at Old Trafford next month.
The last-16 tie is finely-balanced at 1-1 and Ferguson said: "We are working very hard. He has an outside chance for Madrid - but no more than that.
"He is a young man who went into a tackle too brave and was unbalanced.
"He certainly won't be fit for this weekend. As for Real, we will have to wait and see. It is two weeks away and a lot can happen in that time."
The United boss admits Jones - used in attempt to shackle Cristiano Ronaldo in the first leg - is currently an important member of the squad, comparing him with another former Old Trafford great.
He added: "He has the courage and willingness to tackle. Bryan Robson was exactly the same.
"Bryan couldn't see danger and neither can Phil. That is a lot to do with the courage they have. You are not going to take that out of them. I wouldn't even attempt that.
"The great thing Phil has got is that he doesn't care who he is playing against. There is no fear about playing against anyone."