Hargreaves has made only one brief substitute appearance in the last two years, and there are serious concerns over his future career.
He returned to Colorado over the summer, to work with knee specialist Dr Richard Steadman as he looks to save his career.
Hargreaves was included in United's 25-man squad for the Premier League, but his omission from the European selection indicates that he is unlikely to return to action this year. United's final Champions League group game is against Valencia on December 7.
Bebe's omission is rather more curious. Clubs are allowed to name a maxiumum of 25 'List A' players, but United have included only 24. Bebe would qualify as one of the unlimited 'List B' players, as he is under 21, but UEFA stipulate that anyone on that list must have been at the club for two years.
United signed the Portuguese forward for £7.4million in the summer, despite Sir Alex Ferguson never having seen him play.
He was subsequently left out of two United reserve matches, after reports suggested Old Trafford coaching staff didn't consider him ready for even their second string.
Sir Alex Ferguson was furious at these reports, claiming Bebe's omission was a fitness issue, and banned several journalists from Old Trafford.
However, leaving him out of the Champions League squad altogether, preferring to leave a gap in the line-up, suggests he is not of the required standard yet. United have so far offered no explanation for the decision.
Belgian defender Ritchie de Laet is the only other notable absentee from the list.
Full United squad: Van der Sar, Kuszczak, Neville, Evra, J.Evans, Ferdinand, W.Brown, Smalling, Vidic, O'Shea, Nani, Anderson, Giggs, Park, Carrick, Scholes, Fletcher, Valencia, Gibson, Berbatov, Rooney, Hernandez, Owen, Obertan.
'List B' players: Macheda, Amos, Fabio, Rafael, Corry Evans, Oliver Gill.