United have already signed Romelu Lukaku and Victor Lindelof, City have bought Kyle Walker, Ederson and Bernardo Silva, while Chelsea have brought in Tiemoue Bakayoko and Antonio Rudiger.
And it is for that reason why Neville believes Chelsea can not be considered favourites in his eyes.
"Last season they had the best squad and I think this year they've got the best squad again", he told talkSPORT.
"It'll be interesting to see how Chelsea cope with the Champions League, but I can definitely see United and City contending for the title". Not in a negative way, but just having the Champions League will bring different challenges.
The Sky Sports pundit predicts that the race will be between former club Manchester United and rivals Manchester City at the end of the season, and that whichever of the two sides as the best summer in terms of recruitment will shade it. All the clubs are going for the same players, they're all expensive and controlled by agents.
"So, whoever has the best relationship, the best contacts and is willing to put the money in will probably do it".
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"United need to strengthen, but they all do - quite a bit", he added.
City finished third last season, winning no silverware, while United placed sixth but won the League Cup and Europa League.
Quinn believes Pep Guardiola's side are the favourites for the title but says none of last season's top six should be ruled out of contention. All big clubs want to be winning Champions Leagues.
He then struggled to justify his price tag for much of the campaign, scoring just five goals and providing four assists in 30 Premier League appearances for the Red Devils.
"That won't happen unless they significantly improve".
Gary Neville has given his thoughts on Manchester United's transfer window so far, insisting that Jose Mourinho will need to invest further over the next month or so.
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