No chance of top 4 so they are out of the Champions League, but there is a reasonable chance of qualification for the Europa League.
Assuming the top four are Manchester City, Chelsea, Liverpool and Everton, then Arsenal would get the 5th place Europa spot. But they might get that by winning the FA Cup . Manchester City have qualified for the Europa, but if they qualify for the Champions League they won't take that place. Unlike the FA Cup, the League Cup runners up do not get the Europa spot the highest placed Barclays Premier League team qualify. So United could come 6th behind Arsenal and qualify for the Europa Leage with the FA Cup runners up.
United's fate rests on Everton beating Arsenal to the Champions League place and Arsenal winning the FA Cup.
However, I would rather United missed the Europa place as it is a lot of bother for not much reward.