The 23-year-old has been struggling with a muscle tear in his shoulder since November.
Rashford has played through pain for both the Red Devils and England.
An operation on his left shoulder has looked likely, but United are keen to avoid it if possible, as surgery would rule the forward out until October, missing the first few months of the new Premier League season.
Senior officials at Old Trafford had hoped that a three-week holiday after England’s Euro 2020 exploits, would be enough rest for the injury to ease.
That could still be the case, but the Daily Mail reports Rashford still feels surgery is the most appropriate course of action to fix the problem.
A scan showed the tear is unlikely to become any more severe, but Rashford was playing with painkilling injections last season, so it is far from ideal.
A decision could be made on Tuesday when Rashford meets with United boss Ole Gunnar Solskjaer, five days before he was due to return to pre-season training on Sunday.
