The two rivals meet in their first encounter of the season at Old Trafford on Monday in a match neither can ill-afford to lose.
United will draw level in the table with Arsenal if they can snatch all three points, but a win for the Gunners would see them move back into the Champions League spots.
But Graham thinks it will be difficult for the north Londoners to stay there, and doesn’t seem them or United competing for the title for some time to come.
“I can’t see either challenging at the top for three seasons at least,” Graham told the Mail .
Graham led Arsenal to the league title twice in his nine-year tenure as manager, with stars such as Gunners legend Tony Adams in his ranks.
He pointed to a lack of leaders in the Arsenal squad as to why they won’t mount a serious challenge – using Adams and Liverpool’s Virgil van Dijk as examples.
United signed Harry Maguire in the summer, who Graham feels could be the answer for the Red Devils, while Arsenal moved for the experienced but error-prone David Luiz.
But he feels his old club could have the measure of United when the two teams collide, and states that the onus is on the home side to get a result.
He added: “United are under greater pressure because expectations there are higher, both for results and the style of play. It could be a good time for Arsenal to play them.”