Manchester United could face a tough Champions League playoff against AS Monaco or Lazio when the playoff round draw is made on Friday.
United could also face a difficult long-haul journey to take on CSKA Moscow, with Belgian outfit Club Brugge and Austrian side Rapid Vienna completing the list of possible opponents.
Wednesday's second-leg ties in the non-champions route saw Shakhtar Donetsk, CSKA and Brugge seal the final three places in the final qualifying round.
United, Valencia, Bayer Leverkusen, Shakhtar and Sporting Lisbon are the five seeded teams in the draw, which takes place at 11 a.m. BST (6 a.m. ET), and cannot be drawn against each other. The two-legged ties will be played on Aug. 18/19 and 25/26. The winners will advance to the group stage.
Monaco knocked Arsenal out of the Champions League at the round of 16 stage last season, before being eliminated in the quarterfinals by eventual runners-up Juventus. The Ligue 1 side are ranked 68th as they were without European football for several years, but that masks the ability of their current team.
Lazio, who finished third in Serie A last season, are ranked 40th and are back at Europe's top table for the first time since being eliminated at the group stage in 2007-08. CSKA Moscow, who have featured in the Champions League regularly, are 34th.
Austria's Rapid Vienna are the lowest ranked side United could face, sitting 121st in UEFA's coefficient table, with Club Brugge ranked 51st.
Louis van Gaal's side will be in pot 2 of the group stage draw should they advance through qualifying.
Celtic will be one of the five seeded teams in the champions half of the draw, alongside FC Basel, APOEL, BATE and Dinamo Zagreb.
NON-CHAMPIONS ROUTE:
Seeded: Manchester United, Valencia, Bayer Leverkusen, Shakhtar Donetsk, Sporting Lisbon
Unseeded: CSKA Moscow, Lazio, Monaco, Club Brugge, Rapid Vienna
CHAMPIONS ROUTE:
Seeded: FC Basel (SUI), Celtic (SCO), APOEL Nicosia (CYP), BATE Borisov (BLR), Dinamo Zagreb (CRO)
Unseeded: Maccabi Tel-Aviv (ISR), Partizan Belgrade (SRB), Malmo (SWE), FK Astana (KAZ), Skenderbeu Korce (ALB)