Ralf Rangnick says Manchester United "need to be realistic" about their chances of qualifying for the Champions League.
They sit in sixth place, six points behind the Gunners having played a game more than Mikel Arteta's side, meaning that new manager Erik ten Hag will be playing in the Europa League next season, at best.
United face third-place Chelsea at Old Trafford in Thursday's rearranged game having been further hit by the news Harry Maguire and Jadon Sancho have joined the Red Devils’ lengthy list of absentees.
“I don’t think it makes sense now to still speak and speculate about the Champions League,” interim manager Rangnick said. “We need to be realistic.
“Even if we win all four games, it’s still not in our own hands. But what is in our own hands is the way that we play, the level of performance.
“Even for the next season it’s important to finish this season on the best possible note.”
Asked how failing to qualify for the Champions League will impact on United’s summer transfer business, he added: “Of course it would be better if we play Champions League next season, but this also affects other clubs. This is not a problem that only Manchester United has.
Arsenal 3 Manchester United 1: player ratings
“The renewal of the contract of Bruno [Fernandes] showed that it’s still possible – this club is an attractive club and with a new manager.
“With a new approach with a new manager and the way he wants to play, this is still a massively interesting club.
“I am looking forward to helping both Erik and the club, and everyone at the club, to get the best and to change the whole approach again next season so that Manchester United can be a top club again.”
Midfielder Paul Pogba, striker Edinson Cavani and left-back Luke Shaw remain absent against Chelsea, so too does midfielder Fred after a negative reaction after returning to training.
Full-back Aaron Wan-Bissaka is also a doubt for the match..
Meanwhile, Chelsea manager Thomas Tuchel has insisted he will put a competitive Chelsea team on the pitch next season irrespective of who takes over as the club's new owners.
Toni Rudiger will leave Chelsea this summer, with Real Madrid poised to confirm the Germany defender’s switch.
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The 29-year-old will quit Stamford Bridge on a free transfer alongside fellow defender Andreas Christensen, who is on the move to Barcelona.
Asked about Germany international Rudiger's decision to leave, Tuchel said: "I don't think anybody likes it. He gives everybody confidence in the dressing room.
"He is a unique character and plays on an outstanding level. He sometimes takes the focus towards him, he loves responsibility.
"Nobody likes this decision but we have to accept it. Like it or not there will be life at Chelsea after Toni. It is also the most important thing for us that it ends like it started, on the highest level."
Asked about the possible financial constraints after Roman Abramovich's time as club owner comes to an end, Tuchel added: "It is my job [to deal with it]. No matter how the situation is solved and how active we can be in the transfer market, at the end we will dig in and we will try to squeeze out everything from the squad that we have."