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."