Recent reports have linked Rashford with a move to Los Blancos as he struggles to nail down a place in the Manchester United XI.
It’s been claimed that Real Madrid want the England striker as well as Tottenham midfielder Christian Eriksen.
And now the Sun report that Rashford is open to a deal if he is continually denied a space in Mourinho’s side.
It’s been claimed that Real have made contact with Rashford’s representatives as they ramp up the pressure on the 21-year-old.
Rashford reportedly doesn’t want to leave his home town but is concerned he is not going to reach his full potential at United as it stands.
The forward has started five of 12 Premier League games this season, scoring just twice.
He is out of contract at the end of the season but is currently believed to be valued at £50million.
Former Premier League striker Dean Ashton believes Rashford should stay at Old Trafford and not join Real Madrid.
“He has to affect the game, whether that be with deliveries, whether that be linking up with the forward, whether that be running in behind,” Ashton said on talkSPORT.
“I just don’t feel as if he has been that good to earn the spot and be a regular for Manchester United yet.
“But that’s not a huge problem, he’s been playing for England and playing really well.
“It looks like he’s still enjoying his football, he is undoubtedly going to learn a lot from Jose Mourinho because he is a top-quality coach.
“So I wouldn’t be worried if I was him, I wouldn’t be looking elsewhere, certainly not yet anyway.
“I’d be more concentrated on ‘when I get my chance that I play well enough to own the spot that I want to play in’.
“If he wants to play centre-forward, he has to be so good you can’t drop him.”
Manchester United’s next game sees them host Crystal Palace on Saturday (3pm).