Wenger played down the prospect in the immediate future due to his apparent uncertainty over his next destination and - mischievously - Mourinho's.
However, the Chilean, who forced his way out of the club during the winter transfer window, was seen embracing his former manager in an emotional manner.
Sir Alex Ferguson was present at the dugout to greet his old foe before the match, handing over a boxed gift - with Wenger saying immediately after the game: "I don't know [what it is]".
Ferguson told the United website ahead of the game that his clashes for many years with Wenger's strongest Arsenal sides over a decade ago "made the Premier League". You can know their level, but you see what they can produce.
Arsenal's defence has been notoriously brittle this season, but this was a robust team performance full of hard work and occasional attacking flair that looked like earning them a point. "It is very classy from them", Wenger offered after the game, jokingly adding, "When you're not a danger any more, people love you". They had a nice gesture before the game, it was the first time I got a trophy before the game. "Next year, someone else will be in the dug-out and it will be a hostile environment again".
However, Marouane Fellaini scored a last-gasp victor to earn United all three points and seal their place in next season's Champions League.
"I think if it was a draw it wouldn't be unfair".
"We had chances and on the counter we did not use our opportunities as well as we could have".
Current United boss Jose Mourinho, who has also had a rocky relationship with the Gunners manager, joined the duo.
"I am happy with the class my club showed to him", Mourinho said. "I only played Mr Wenger three or four times as United manager".
The result ensured Arsenal can not finish above north London rival Tottenham and guaranteed United a top-four finish and a spot in next season's Champions League. It would mean more for Alex to do it.
Manchester United manager José Mourinho has confirmed that Belgium global Romelu Lukaku could be forced to miss the FA Cup final against Chelsea next month after the 24-year-old hobbled off the pitch with a foot injury against Arsenal.