Spanish full-back Bellerin ruptured his anterior cruciate ligament in the 2-0 win over Chelsea last time out and will miss the rest of the season.
Mkhitaryan, who hasn't featured since early December, remains unavailable to face his former club as he is recovering from a fractured metatarsal.
Unai Emery opted for wholesale changes in the previous round as the Gunners saw off Blackpool but is expected to field his big guns against United, although Petr Cech could start in goal ahead of Bernd Leno.
Arsenal are likely to come up against former forward Alexis Sanchez on Friday as he has recovered from a hamstring problem.
Emery revealed he tried to sign the Chilean during his time in charge of Paris Saint-Germain, and he says his defenders will have to be on top form to keep Sanchez and United quiet.
"He's been starting on the bench after an injury but if he plays Friday, we need to work to stop him because he is a very good player," he told reporters.
"Now, this team [United] is different. I don't know why. But this team is different and they are playing with more confidence. 'They are winning their last matches and whether he is playing with one player or another player, they are with big performances."