Ajax lost 3-2 at the Amsterdam ArenA to go out 5-2 on aggregate – a result that helps United by removing the four time European champions from the list of potential opponents they could be paired with in the final play-off round.
Unted will be seeded in the ‘league route’ side of the draw alongside Valencia and Bayer Leverkusen.
Ajax would also have made it into the seeded pot if they had progressed, but Rapid’s lower UEFA co-efficient score means Sporting Lisbon will be in the group of teams United cannot face instead.
Shakhtar Donetsk will be the final seeded side if they beat Fenerbahce on Wednesday night – but CSKA Moscow will take their place if they get through and the Shakhtar lose out.
If Wednesday night’s games go to form, United’s list of possible opponents in the draw will be: CSKA Moscow, Lazio, Club Brugge, Monaco and Rapid Vienna.
In Tuesday night’s other qualifying games, Monaco hammered Young Boys 4-0 to go through 7-1 on aggregate, APOEL Nicosia beat Midtjylland 2-1 on aggregate, Dinamo Zagreb knocked out Molde on away goals after a 4-4 draw.