Palace are close to beating the drop after victory at Cardiff City.
"He is definitely up there," said Jerome.
"Jose Mourinho said last week, from where we were to where we are now speaks for itself.
"It's not necessarily the manager that wins the league who is the best, it's the one who has done the best job.
"I think with the resources he has got, the amount of people that have written him off, Tony has done an unbelievable job.
"He deserves every plaudit that he gets. He had a point to prove coming here and he's the sort of man who relishes that sort of challenge.
"If he manages to keep us in the Premier League, he will have done a fantastic job."
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