Graham feels that the unrest surrounding Rooney could have something to do with his fitness.
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."
Graham also felt that the England striker has to remain "disciplined" away from the field as well as on it.
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."