The Portuguese hit back at his counterpart in February for branding him "afraid to fail" after repeated assertions that his then-table-topping Chelsea side were not favourites for the Premier League title.
He told reporters: "I didn’t get an apology so I don’t apologise. My feeling is to get over it, forget it and to move forward without thinking about what happened, you don’t need to apologise.
"I don’t need to get an apology, I don’t need to apologise. Football people, intelligent people we don’t need that. Finish, move and let’s go for another match with a big responsibility for both of us.
"We manage two big clubs in London and have responsibility to have a good football match for millions of fans that both clubs have and the League has. So no problems."
Arsenal travel to Stamford Bridge on Sunday for the first time since a humiliating 6-0 loss in Wenger's 1000th game in charge, but Mourinho sees no reason to dwell on the result despite expecting to win again.
"The 6-0 is once every 50 years," said Mourinho. "Me against Arsene Wenger? I never had the pleasure to play one-on-one against him. It's Chelsea and Arsenal and even that doesn't play a part.
"What happens in the past, is the past. It's a difficult match against a good team."
"I expect a difficult match, it doesn’t matter their approach or what they try to do. They will always be a difficult opponent. But I always expect [to win] every game, every opponent. Nothing changes that."