The Premier League side have appointed Jose Mourinho as their new boss.
Hull City manager Steve Bruce
The Red Devils have announced that Jose Mourinho will take over from next season after the Dutchman endured a mixed spell at the helm.
But after watching Bruce lead Hull City back to the Premier League at the first time of asking as they beat Sheffield Wednesday in the play-off final, Holloway claimed that United should have thought about their former defender and captain as a possible candidate.
He told Sky Sports: "I know they were talking about Manchester United and who was going to get it, and I know Jose Mourinho did, but seriously, why doesn't someone like Bruce get considered?
"It's only a matter of time before people like Steve get appreciated at the top level of this game and just given a chance."
Bruce's record in the Championship is hugely impressive, with Saturday's victory seeing him secure promotion for the fourth time since becoming a manager.
However, his lack of experience at the highest level in the top flight would have made him the kind of gamble that appointing Mourinho arguably does not present.
While most managers need to be given a chance if they hope to prove themselves, the United hierarchy are perhaps reflecting on David Moyes' tenure as proof that making the step-up can be too big a challenge for some and thus, they would be better off going after the former Chelsea boss who has delivered at practically every club he has been with.
But if Bruce manages to oversee a fantastic campaign with the Tigers next term, then perhaps it will become too difficult for the bigger clubs in the division to ignore him.