The great thing is that the biggest problem is the guy who picks the manager.
Even if they do get rid of Mourinho though, a good manager will need to gut the squad.
- They've a bunch of old players - Valencia, Young, Matic, Fellaini, Sanchez, Mata would all be over 30 next summer. Can't build around any of them.
- They've a bunch of poor players - Rojo, Smalling, Shaw, Darmian, Herrera.
And then there's people like Lingard who is doing well for them because working hard = good in a Mourinho side, but wouldn't get in another top 6 team.
Even if a great manager came in and got backing they'd have to buy 3 fullbacks, 1 leader at CB, a RW and another midfielder so Fellaini isn't your first choice replacement.
Then you have to try and repair the players Mourinho's sent backwards. Shaw is probably beyond repair, but Lindelof & Martial might be salvageable.
That's a 2 year project before you're competing.