The Portuguese is the subject of a new biography in which he is quoted as saying he would break Wenger’s face.
Asked if it is true that he made the comment, Mourinho said: “No, I met Arsene Wenger a couple of weeks ago and like civilised people we shook hands, we sat on the same table.”
Mourinho described Wenger, 66, as a “voyeur” in 2005, after his rival questioned Chelsea’s transfer policy.
The former Real Madrid boss referred to Wenger as a “specialist in failure” in February 2014 after the Frenchman said other Premier League managers were playing down their title chances because they “fear to fail”.
In the aftermath, Mourinho is quoted – in a book serialised in the Daily Mail – as saying: “I will find him one day outside a football pitch and I will break his face.”
Mourinho played down the contents of the book, which details alleged conversations with a football journalist, adding: “I don’t think it will be in the gallery of the Shakespeares and so on and I prefer just to not comment.
“It is my last word about it and again I repeat, he is making his money. That’s fine by me.”
Wenger, who apologised for pushing Mourinho during a 2-0 defeat by Chelsea in October 2014, said: “I have no personal problem with anybody. I respect everybody in our game.
“What is amazing is that this has nothing to do with our game. I am just focusing on doing my job well and respecting everybody else.
“Maybe I will make a book one day but I am not ready for that yet.”
Manchester United host Leicester at 12:30 BST on Saturday in the Premier League while Arsenal entertain Chelsea at 17:30.