The Arsenal boss has never beaten Mourinho in the Premier League but will be hoping to strike lucky at the 13th attempt when the Portuguese takes his Manchester United side to the Emirates Stadium on Sunday.
The pair have clashed both verbally and physically since Mourinho's arrival at Chelsea in 2004 and their touchline antics have long-been a sideshow to any meeting of their respective teams.
Sunday's game is arguably bigger for Wenger, who has still yet to announce whether he will sign a new deal to remain at Arsenal beyond the end of the current season.
The 67-year-old has seen a minority of fans begin protests against a new contract being offered after a run of poor form left the Gunners out of the Premier League top four and humbled by a 10-2 Champions League aggregate defeat at the hands of Bayern Munich.
Wenger has guided Arsenal to a third FA Cup final in four years but that has done little to curtail calls for his exit, especially after Sunday's 2-0 north London derby defeat at Tottenham means Spurs will finish above their neighbours for the first time since 1995.
Mourinho visits either side of a Europa League semi-final clash with Celta Vigo and, despite United still harbouring their own ambitions of a top-four finish, he said on Wednesday he may rest some of his key players on Sunday.
But away from the pitch, Wenger is prepared to call a truce with Mourinho, in a similar way as he did with Sir Alex Ferguson when the pair were fighting for titles.
Asked whether his relationship with the former United boss mellowed over time, Wenger replied: "Mellowed? Yes
We have respect.
"I think I try to respect everybody and I do not want to make a case of any person
I think it is important that I focus on my own team, the performance of my team and forget all the rest."
When questioned on whether amicable ground could be found with Mourinho, he said: "I am open always in life for everything, you know, for peace.
"But what is important when you are a competitor is that you give absolutely everything to win the next game."
During the Wenger and Ferguson rivalry, meetings between Arsenal and United would often dictate the destination of the title.
Heading into this weekend, Arsenal are sixth with their visitors just a place above them in fifth, with Wenger admitting other clubs have now caught up with the duo
"It just shows that everybody has moved up," he said
"The number of clubs that can fight at the top is bigger this season and the difference between the teams is smaller
As soon as you are not at your best you can lose."
United's fate immediately after Ferguson retired following 26 years as manager has often been portrayed as a warning for what Arsenal could expect when Wenger leaves
The Red Devils have made the top four only once in the three full seasons since his departure, despite spending vast sums of money.
But Wenger said: " It can as well go better from when I leave one day
"You know, when you are such a long time at a club like I am, like Ferguson was, it is a little bit like when you have children
You want them to be happy
Even when you are not there anymore, you want them to be happy."
He was adamant Arsenal would not shift their summer transfer targets if they failed to make the Champions League and claimed he would follow Mourinho in taking the Europa League seriously
The Frenchman added: "It means we focus on the same players
I take every competition seriously
The only thing I always did over the years was to use the League Cup to give chances to young players
We always treated all the other competitions seriously."
Source : PA