United finished sixth last season, but kicked off this new campaign with a 4-0 win over West Ham on Sunday.
Neville won the league eight times with United and he says his former club must now challenge again.
“You can’t just drop your expectation because they haven’t won it for a couple of years. They have to win the league. Jose Mourinho has to win the league here,” he said on Sky Sports on Nissan Super Sunday.
“The money that’s been spent, his own personal expectations and what he’s always delivered has been titles, so I would say United have to approach this season to win the league.
“I don’t think it’s good enough to say ‘they’re going to get back into fourth’. That isn’t an ambition when you’ve spent the money that’s been spent and amassed the players that Mourinho has now amassed.”
United have not won the Premier League title since 2012/13 when Sir Alex Ferguson retired.