The Red Devils ultimately ended the 2016-17 season on a high by adding the Europa League crown to their earlier EFL Cup triumph, papering over what was a poor Premier League campaign by their high standards.
United finished a lowly sixth in the top flight, seven points off the top four and 24 points adrift of champions Chelsea, but Neville insists that Mourinho will not settle for anything other than top spot next term.
"It's going to be a difficult season, as everyone else is spending money and improving," he told MUTV. "United are going to have to improve as well because they didn't finish in the top four last season.
"Even that is a big ask, but I think Jose will want to win the Premier League. That's the big one. He won't settle for anything less. Now we're looking to see who Jose signs because, if you look at the top six clubs, I think they will all strengthen.
"United have to strengthen and it'll be interesting to see which team strengthens the most. If you look at the drawn games at Old Trafford last season and convert maybe 90 per cent of those into wins, then United would have been challenging for the title. If they can do that this year, then I think the title will come back to Manchester."
United begin their Premier League campaign with a home match against West Ham United on August 12, before travelling to Swansea City a week later.