Can Any Manager Win The Premiership On Arsenal’s Budget?

I realize this is a radical question that can easily be misinterpreted as being defeatist or lacking ambition. But that doesn't take away the fact that apart from Wenger no one has come close to winning the Premiership on Arsenal's budget. Even then if we accept for a moment that Arsene should go, it's important to consider who can come in and deliver the big trophies.