The Blues boss was responding to the Arsenal manager's claim the Premier League title is "Chelsea's to lose".
Chelsea hold a one-point advantage over the Gunners, with Manchester City a further two points back.
Mourinho on Wenger
Under Wenger, Arsenal have not won a trophy since 2005 and Mourinho said: "Eight years without a piece of silverware, that's failure."
Mourinho continued: "He is a specialist in failure. I'm not. So if he is right and I am afraid of failure it is because I didn't fail many times."
"The reality is he's a specialist because eight years without a piece of silverware, that's failure. If I do that in Chelsea, eight years, I leave and don't come back."