The former Arsenal, Tottenham and Leeds manager believes that last season's top two will remain the front-runners but acknowledged that the London sides are improving
The 67-year-old believes that the strength of reigning champions Manchester City's squad and the experience of Manchester United manager Sir Alex Ferguson will ensure that the two clubs are in contention for the title again.
"I just feel that, one way or another, the title will stay in Manchester," Graham told the Sunday Mirror. "City have not yet made any expensive buys, but when you look at it, do they need to?
"In David Silva and Sergio Aguero they have world-class players and Carlos Tevez is still there. The goalkeeper Joe Hart is the last line of a well-organised defence, and they have a strong midfield.
"United? They need to strengthen and I think Sir Alex Ferguson knows that.
"But they still have Wayne Rooney, Danny Welbeck and Javier Hernandez as well as Ashley Young and Nani. They will be a big force."
Graham managed Arsenal to two league titles in the 1988-89 and 1990-91 seasons but does not see the north London side challenging for the title during the 2012-13 campaign.
Arsene Wenger moved to bring in talent early in the transfer window and Graham hopes that they can find their feet quickly in the Premier League to secure a place in the top four.
"[Arsenal are a] real contender for the top four," he continued. "I am told Santi Cazorla is a real talent and they also have Lukas Podolski and Olivier Giroud up front.
"Maybe [settling in] it's not such a problem for Podolski, because he has been playing in Germany and that is similar to our football.
"He didn't have a great European Championship, but he, for me, was played out of position, in a wide left role. Giroud might find it harder, because French football is not so demanding."
Tottenham, meanwhile, have made a change in the managerial department, with former Chelsea boss Andre Villas-Boas replacing Harry Redknapp in the White Hart Lane dugout.
And Graham thinks the gamble to replace the successful 65-year-old could work out for Spurs chairman Daniel Levy.
"He has had just two jobs in football at the top level," he opined. "He did a magnificent job at Porto. He was brilliant.
"Maybe he wasn't given much time at Chelsea, so you could say the jury is still out on him. But if it goes well, then Tottenham could well push for a Champions League place."
Chelsea have undergone a recruitment drive of their own since claiming the Champions League trophy at the end of last season, but Graham - who used to play for the Blues - does not think they will challenge for the league crown immediately.
"I still think they will be short of what is needed to pick up the title," he concluded.
"Di Matteo must decide how they are going to play. They seem to have brought in quick, nimble players and it will be interesting to see the style they adopt.
"Is it going to be like Barcelona, with neat, quick passing? Or will they stick to what brought them success last season?"
Graham was impressed, in addition, by the appointment of Brendan Rodgers at Liverpool, but recognised the step up the Northern Irishman faced at Anfield.
"I have a lot of time for Brendan Rodgers," he admitted. "He had a tough time in his first managerial job at Reading, and maybe he tried to change things too quickly.
"But he showed his ability at Swansea, who were great to watch last season. But Liverpool is a different world. A really big club. I hope he does well. And I hope he is given time."