Rooney's future has been the subject of intense speculation this week after the England striker was omitted from the starting line-up for Tuesday's Champions League defeat by Real Madrid.
Manager Sir Alex Ferguson has insisted there are no problems and the 27-year-old will not be leaving Old Trafford - but Rooney's future remains the subject of widespread debate.
Graham, who guided Arsenal to two league titles, believes Rooney's fitness and off-field lifestyle could be an issue.
The Scot 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."
He added: "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."
Ferguson has said the club intend to keep Rooney beyond the length of his current contract.
The former Everton forward is tied to United until the end of the 2014-15 season and Ferguson expects a new deal to be discussed.
Ferguson was quoted in several Sunday newspapers as saying: "There's no issue with his contract, when it has to be renegotiated it will be. We don't want players to leave."
Graham, however, is unsure whether Rooney's long-term future lies at Old Trafford.
"I have got a funny feeling it won't be," said the former Scotland international, who had a spell at United as a player.
"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.
"Two years is usually the time you start negotiating again with a new contract.
"Yes, I am sure United will offer him a new contract but it may be less money than he is on now."
Yet should Rooney come to move on, Graham expects options to be limited.
He said: "There are only a few clubs that could afford him - two or three in Italy, two clubs in Spain.
"Even in France now, with their tax situation, I wonder if Paris St Germain could even afford Wayne Rooney."
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