Mourinho has had a series of run-ins with the Arsenal boss over the years and reignited the tension Friday, calling Wenger a "specialist in failure" — referring to the Gunners' eight-and-a-half-year run without silverware.
The barb was aimed at Wenger after the 64-year-old said it was about time Chelsea was seen as the title favorite, suggesting Mourinho's fear of failure was the reason he continually plays down expectations around the club.
Yet Mourinho refused to quell the storm, telling ITV prior to Chelsea's 2-0 loss at Manchester City: "When he says that I am afraid of failure he is not respecting my past and because he does not respect this I do not respect his past.
"That’s my answer. It’s an answer that doesn’t make me happy, but an answer that I think he deserves."
The Blues were defeated convincingly by Manchester City on Saturday, as goals from Stevan Jovetic and Samir Nasri dumped Mourinho's team out of the FA Cup.
Arsenal, meanwhile, is still chasing that elusive piece of silverware and hosts Liverpool in the fifth round of the FA Cup on Sunday.