I cannot believe that this question is actually being asked but it is being suggested in some quarters and is therefore worth a debate.
Personally, I would say no way, there are too many high-quality managers out there for the club to hire in the event that they part company with Unai Emery.
Forget all the personality stuff and the clashes with Arsene Wenger down the years, that is what managers do to each other and anyway, Mourinho and Wenger do punditry together, no, my issue is with his qualities as a manager.
Yes, he has been a serial winner but he is not a long term manager, he tries to buy success, he has no record of developing youth, he plays awful football and his tenure at United in terms of league success was poor.
Mourinho is the sort of manager that requires all the tools, he has to have it handed to him on a plate, he is not a builder of teams and that is not what Arsenal fans want in a manager.
He is far too controversial and it always ends up being about him and not the team, he alienates players and is basically a disruptive influence.
That is why I do not feel he would be a good fit for Arsenal.
Unai Emery may still turn things around at Arsenal but if he does not, there are managers like Massimiliano Allegri or even Rafael Benitez that would be a far better fit as an Arsenal manager than the divisive Mourinho.