Hopes are high at Stamford Bridge that the appointment of Jose Mourinho can help the Blues lift their first Premier League title since 2009-10.
And Neville feels the Portuguese tactician's return to west London, and the fact that United will be embarking on their first league campaign with new boss David Moyes at the helm, means it is imperative the champions do not lose pace early on.
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"At United we weren't slow starters particularly, but we generally weren't at our peak from September to December and, in those Mourinho years, we'd fall too far behind them to mount a challenge when we did get into our stride in the New Year.
"The critical thing is to be in contention at the turn of the year because you don't want to fall too far behind a Mourinho team. They have the nerve inside the club to withstand the pressure.
"We're stepping into the unknown slightly. Going into a new season you think of Sir Alex Ferguson and automatically think Manchester United will be up there.
"A Jose Mourinho team will be there or thereabouts, always. But we're actually going into a campaign for the first time in a long time where we're not quite sure what's going to happen: how everyone's going to react to new manager, to new squads, to new signings."
Neville also spoke about unsettled striker Wayne Rooney, who has been the subject of much speculation regarding his playing future this off-season.
The 27-year-old was forced out of United's pre-season tour of Asia on Thursday with a hamstring problem, but Neville feels he will stay in Manchester.
"Wayne Rooney and Manchester United go together," he said. "I'm aware of how big the football club is, and the fact you can achieve all your ambitions there.
"But Wayne is ambitious himself. He has to make his own mind up. There have been rumblings about Wayne but he has come back into pre-season without much of a fuss, and this will unfold in the next few weeks.
"He has been too good a player - a great player for Manchester United - for the fans not to accept him.
"Obviously, they want players to be committed to the club, but one thing about Wayne Rooney is, wherever he plays his football and whatever is going on, he is always 100 percent committed to what he does."