The Portuguese has stated on a number of occasions that his side are not favourites for the title - a stance Wenger believes shows his rival's "fear to fail".
With just a point separating their respective sides in first and second in the Premier League table, Mourinho hit back at the Frenchman, whose team have not won a trophy since the 2005 FA Cup.
"He is a specialist in failure. I don't fail many times - maybe he is right, maybe I am not used to failure but the reality is he is a specialist," Mourinho said.
"Eight years without silverware, that is a failure. If I do that at Chelsea I don't come back."
Chelsea travel to Manchester City for an FA Cup fifth round clash on Saturday, with the Londoners having come out on top in their Premier League meeting at the Etihad Stadium earlier this month.
Mourinho insisted that the competition remains a priority for him, before responding to comments from City counterpart Manuel Pellegrini following a number of spats in the media.
"Our priority is always the next match, even in the (League Cup) we lost against Sunderland but it was a priority for us," he added.
"I don't like this talk of records between managers, because it is between teams.
"If I have the record in favour or against (Pellegrini), I don't like both ways. If he doesn't like to speak about me then perfect, I hope he does what he says and doesn't talk about me."
