A surprise announcement last week confirmed Wenger will end a spell of over 21 years as Arsenal manager when he steps down at the end of the season.
The 68-year-old has had a number of unsavoury spats with Mourinho since the Portuguese took over at Chelsea in 2004 – with the rivalry between the pair often leading to verbal – and sometimes physical – altercations.
Wenger had not beaten Mourinho in a competitive fixture until a 2-0 win over Manchester United towards the end of last season.
While the two have clashed in the past, Mourinho spoke warmly about Wenger following his announcement and has since suggested they could “even be friends in the future”.
The Gunners travel to Old Trafford either side of their Europa League semi-final against Atletico Madrid, with the tie finely-poised after a 1-1 draw at the Emirates Stadium on Thursday.
Wenger was asked about Mourinho’s kind words and whether he felt an unlikely friendship could be struck up at some point.
“It depends,” he said. “I respect him of course… you should give me a little bit of peace for my final weeks and not try to push me into another confrontation.
“I want to go peacefully, and with Mourinho now because he is a great manager.
“I say goodbye to everyone. In France we say au revoir which means you might see me again.”
Before Mourinho’s arrival, Wenger’s main feud was with former United manager Alex Ferguson.
The Red Devils battled with Arsenal for the major honours in English football but the two men are now friends.
Former Manchester United chairman Martin Edwards revealed in his 2017 autobiography that he held talks with Wenger over replacing Ferguson at Old Trafford when the Scot originally announced he would retire in 2002.
Ferguson changed his mind and would stay for another 11 years while Wenger, at the time of Edwards’ book launch, said Arsenal’s “values” meant he would not have taken the job anyway.
He added to those comments when asked ahead of his final trip to Old Trafford if he regretted never managing United:
“No, because Arsenal is the love of my life,” he said.
“I turned many clubs down to stay here and face the challenge when we built the stadium.
“I don’t regret that because I see my life and what is important to me.
“Yes, I speak to everybody. Yes, I met Martin Edwards but many people came to see me in my home. But I was loyal to this club.”
Wenger could make a raft of changes at Old Trafford with next Thursday’s Europa League semi-final return leg at Atletico Madrid the priority.
Pierre-Emerick Aubameyang, cup-tied in Europe, is available while Henrikh Mkhitaryan could feature against his former club but may be one of those wrapped in cotton wool having only just recovered from a knee injury.
Mohamed Elneny (ankle) is missing.