Would you allow O'Neill to taint his past record? There's a suspicion that like Mourinho his methods are stuck in the past however...
My list would be;
Dieter Hecking - doing a great job at Monchengladbach at the moment.
Julian Nagelsmann - another thats done a great job in the Bundesliga for Hoffenheim
Can't think of many more and the above two get Champions League football fairly regularly at present so its on the premise that they find the Premier League an appeal.
That's my biggest flaw with the whole Puel in Puel Out debate, there aren't many managers out there I have the confidence in to take us forward. Eddie Howe would be a shout but I'm not sure he would leave Bournemouth after experiencing how that can go wrong previously - and having seen him flop at Burnley all those years ago it makes me question if he can adapt to another environment with different expectations. The same to be said about Dyche.
Other managers that might be worth a look but I don't think have the required pedigree to take us forward;
Chris Wilder is doing a great job at Sheffield United
Daniel Farke is doing bits at Norwich
David Wagner - was on top of a lot of lists last season but I'm less convinced
I think we need to be careful what we wish for, I don't think Puel will get us relegated and we'll be a fairly solid side under him, but it does mean putting up with some poor performances and boring football at times. Would we rather risk it and end up with Mark Hughes? Because lets face it, Souza didn't work out, Eriksson didn't work out, Pearson was the 2nd coming - we got lucky with Ranieri,Shakey didn't work out and Puel hasn't inspired anyone...