Yet that is the target new manager Louis van Gaal has set the team as part of an ambitious three-year plan.
''I hope we are in the top four this season - it suits a club like Man United,'' Van Gaal said Friday, ''and then maybe the next step is to be (English) champions and then the next step is to be the winners of the Champions League.''
Those comments could invite ridicule considering how United performed last season under David Moyes and started this season under Van Gaal.
After earning just one point from Premier League matches against Swansea and Sunderland, United lost 4-0 to third-tier MK Dons in the second round of the League Cup on Tuesday.
Suddenly, the World Cup in Brazil - where Van Gaal led the Netherlands to the semifinals last month - seems a dim and distant memory.
But Van Gaal is used to making bad starts at club level.
Van Gaal's Barcelona was 10th after 14 games of the 1998-99 season but still won the league. In 2009, Bayern Munich was seventh after 13 matches under the Dutchman but ended the season as champions.
''When I started with the Dutch national team (in 2012), no one believed we could qualify (for the World Cup),'' Van Gaal added.
''After that, they said we wouldn't have any chance to get through the group stage, and after that (they said) we'll lose against every opponent.''
Given United's start to the season and the squad depth of Premier League rivals Chelsea, Manchester City, Arsenal and Liverpool, finishing in the top four would be some achievement.
A first win of the campaign would do wonders for confidence and United is hoping that comes Saturday at Burnley, where Argentina midfielder Angel Di Maria is in contention to make his debut after sealing his move from Real Madrid for 59.7 million pounds ($99 million).
''I think he is ready to play,'' said Van Gaal, who is without 10 players because of injury.
It won't be Van Gaal's first trip to Turf Moor. In 1992, he was there as coach of Ajax for a friendly that the Dutch club - then UEFA Cup champion - won 1-0 in front of a crowd of 10,746.
''Yes, I was there!'' Van Gaal said after a moment's pause. ''We won. I took over there in 1991, we won the UEFA Cup in the first season, in the second year we won the (Dutch) cup, and after the league.
''It was a step in the process.''