Rooney was surprisingly left on the bench for Tuesday's Champions League defeat by Real Madrid, triggering massive speculation about his future.
Manager Sir Alex Ferguson attempted to play that down on Friday, insisting Rooney would still be at Old Trafford next season.
Former Arsenal and Tottenham manager George Graham, however, believes Rooney does have a problem with his fitness - and the England forward did fade badly in the second half of the 2-2 draw with Chelsea.
Graham told BBC Radio Five Live's Sportsweek programme: "I think with the build Rooney has got he is always liable to put on weight.
"He has got to play regularly, he has got to play every week.
"He cannot afford to have any bad injuries when he has been out for a long time. I think he has got a problem with his fitness.
"For his career, for the next four years he is going to be at his peak, he has got to be very disciplined not only on the pitch in his performances but he has got to be disciplined off the pitch.
"This is probably a little problem that I am sure has been foreseen by Sir Alex in the past."
Graham is unsure whether Rooney's long-term future lies at Old Trafford.
He said: "I have got a funny feeling it won't be. It is a big call and it might not be Sir Alex's decision, it may be the money men's decision in the background."
Ferguson bristled when asked about Rooney before the start of the cup tie.
Questioned about Rooney's response to being left out in midweek, he told ITV1: "Nothing. It's straightforward. I don't see why you want to ask that question."
To a follow-up question asking whether Rooney 'just has to get on with it', Ferguson responded: "Everyone has to get on with it."
Rooney is tied to United until the end of the 2014-15 season and Ferguson expects a new deal to be discussed.
Ferguson said: "There's no issue with his contract, when it has to be renegotiated it will be. We don't want players to leave."
Sir Bobby Charlton has no doubt Rooney will still be a United player next term.
Reports today have suggested Bayern Munich may be interested in making a move for the 27-year-old this summer, and asked about such talk, Red Devils director and former midfielder Charlton said: "I think that is a bit premature.
"I don't know everything that happens at Manchester United, but I know a little.
"Wayne Rooney maybe has had an injury and has not performed as well as he might have done, but that doesn't mean to say that you get rid of him.
"Sir Alex Ferguson came out and said that he had no intention of letting Wayne Rooney go anywhere.
"You have to abide by that and I believe it, 100%. He is a great player - why should we get rid of a great player?"
Charlton was speaking at a press conference in Rio de Janeiro ahead of Monday's Laureus World Sports Awards.
He was flanked by Bayern's honorary president Franz Beckenbauer, who said: "I would be very, very happy if Wayne Rooney decided to come to Bayern Munich, but is this a rumour or is it true? I don't know!"