Jose Mourinho's side were humbled by current holders Real Madrid in the Super Cup earlier this month but will fancy their chances against other elite competition after a strong start to their Premier League campaign.
We will discover the three teams United will face in the Champions League group stage in the draw which takes place in Monaco at 5pm BST on Thursday afternoon.
Each of the 32 teams will be divided into four pots and then drawn into eight different groups – comprising of one team from each pot.
We already know the composition of Pot 1 – with current holders Real Madrid being grouped alongside the champions of the other top seven leagues in Europe based on Uefa’s coefficient rankings.
In England’s case, that means Premier League champions Chelsea are in Pot 1, while Manchester United and Manchester City are placed in Pot 2.
Tottenham are most likely to find themselves in Pot 3 alongside Liverpool, should they qualify, while Celtic will be in Pot 4.
No team can face another from their own pot or from their own country.
By assuming the top seeds from each play-off tie reach the group stage (ties to be played on Tuesday and Wednesday night), we have a good idea of the best and worst possible scenarios for each of the British clubs in the draw.
Here are Manchester United’s worst case scenarios:
Because United are in Pot 2, they avoid the likes of Barcelona, PSG, Atletico Madrid and Borussia Dortmund - but they could find themselves up against defending champions Real Madrid.
Should they draw Juventus from Pot 1, United will avoid Italian sides Napoli and Roma but could instead face a tough trip to Turkish champions Besiktas.
RB Leipzig, who finished second in Bundesliga last season, appear to be the most challenging opponents from Pot 4, which could also contain Dutch champions Feyenoord and Portuguese side Sporting.
Here are United's best case scenarios:
The lowest ranked sides in Pot 1 (according to Uefa club coefficient rankings) are Russian champions Spartak Moscow and Ukrainian champions Shakhtar Donetsk.