Sixth place earned them entry into the group stages, but everything could change if Watford win their first major trophy at Wembley.
Should Man City win their FA Cup final against Watford on Saturday, Wolves - who finished seventh in the league - would qualify for Europe for the first time since 1980. They would be granted entry in the second qualifying round of the Europa League, allowing United to enter the competition directly in the group stages.
So if Watford pull off a massive upset against the Premier League champions, they would be awarded a Europa League group stage spot ahead of Man Utd and Wolves would miss out entirely.
Man Utd, as consequence, would then forced to enter in the second qualifying round instead of being allowed to begin in the group stage, which starts on September 19 – well after the new Premier League campaign begins, with no requirement to play further fixtures in the summer.
Having to participate in UEL qualification will cause further fixture congestion for United's already busy pre-season schedule.
The second qualifying round commences on July 25, which is the same day that they are due to play against Tottenham in Shanghai in the International Champions Cup (ICC).
Should Watford win the FA Cup, Solskjer's side faces a conundrum as they will have to re-jig their pre-season commitments and either pull out of their ICC fixtures altogether, or potentially split their squad between China and Europe.
They could also look into moving the fixture against Tottenham to Europe, though both teams are due to play in Singapore a few days later.
Being required to play in the Europa League play-offs would be even more of a disappointment to Solskjaer, after the Red Devils spent most of the campaign fighting for a spot in the Champions League only to lose out on fourth place by five points.
A similar clash of fixtures happened back in 2015 when newly-appointed West Ham boss Slaven Bilic. The Hammers boss had academy director Terry Westley oversee a Europa League qualifier, while a handful of first-team members continued with their pre-season preparations in Ireland instead of featuring in the game at Upton Park.