United travel to Southampton on Sunday for the final game of what has been a truly wretched season.
The same squad that won the title by 11 points last year looks set to finish the current campaign in seventh
If that is the case, there will be no European football at Old Trafford next year for the first time in almost a quarter of a century.
After such a disappointing year, finishing fourth would be a massive improvement.
But midfielder Michael Carrick thinks United should be aiming much higher.
"There is no way we are settling for top four - that is not something we do here," Carrick said after Tuesday's 3-1 win over Hull.
"We can't celebrate getting into the top four, that's not worth celebrating.
"We want to be challenging right at the top.
"I am not saying we are going to win the league next season, but that is what our goal is and anything less is not worth thinking about.
"Certainly top four is not something that we will settle for."
United's new manager, expected to be Holland coach Louis van Gaal, will be handed a huge transfer £150million transfer kitty to add new faces to a squad which has failed in almost every department this term.
David De Gea, Wayne Rooney and Adnan Januzaj have been the only players to make an impressive contribution to the team all year round.
Luke Shaw, Toni Kroos and Edinson Cavani are all on United's wanted list, as well as Sporting Lisbon midfielder William Carvalho.
Question marks remain over several United players, including Nani, Javier Hernandez, Alex Buttner and Shinji Kagawa.
Interim player-manager Ryan Giggs, who came off the bench against Hull, believes big changes are not required within the playing squad, and Carrick agrees.
The England midfielder feels there is talent in the squad, and he is also optimistic that the likes of James Wilson, who scored twice against Hull, and fellow debutant Tom Lawrence, can make an impact next year.
"It was good to see those two young boys starting
Both of them did so well and they looked so comfortable," Carrick said.
"James will obviously get the headlines because of his goals but I thought Tom was terrific as well.
"This club moves forward all the time and we are always trying to bring players through, groom players and develop them.
"You could say this is the start of something else because there are going to be changes between now and next season.
"It is easy to say there will be wholesale changes because obviously we haven't had a good season
But if you look within the squad, there are some good players there.
"There probably needs to be some changes in some way because that is natural with the situation we are in at the moment, but you can't change too much because it is hard."
Carrick still harbours hopes, meanwhile, of making England's World Cup squad, but team-mate Phil Jones' chances suffered a blow when he was taken to hospital with a shoulder injury during the midweek victory over the Tigers
The extend of the defender's problem has yet to be diagnosed but, with Roy Hodgson naming his provisional squad on Monday, there is little time for the 22-year-old to recover.
"I can only imagine what it must be like, getting injured so late on," Carrick said.
"It didn't look great for him and hopefully it is not as bad as it looks but it is a problem at this stage of the season when anyone gets an injury because you are in danger of missing the summer.
"The only thing you can say is that he is so young and is that good that the chances will come again, but at this stage it is not going to soften the blow for him.
"If that is the case then I am hugely disappointed for him because he obviously doesn't deserve that.
"There is not going to be a team set in stone that is going see the whole tournament through, but for someone to miss out with an injury at this stage is devastating."
While there appears to be others ahead of him in the race for selection, Carrick is keeping an open mind about his involvement in Brazil.
"You just have to wait and see
It is up to the manager now to pick his squad," he added.
"There is no point in me saying anything else, really
There is nothing else I can do - we will just have to wait and see."
Source: PA