The pair famously enjoyed a combustible relationship during the Frenchman's first decade in England, regularly exchanging barbs as their two teams vied for supremacy at the summit of the Premier League.
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"I would just like to pay tribute to an unbelievable achievement and a fantastic career," the Gunners' boss told his Gunners' official website.
"It is difficult to imagine English football without him, but it's now a reality and a fact.
"Of course the next manager has to fill in and show he has the dimension to do that. It is a big task for the guy who comes in.
"What you can say still is that Manchester United are commercially and financially one of the strongest two or three clubs in the world, and that is still a good basis to start when you come in because you know the players are there, the team is there, and the potential is there.
"They have developed very well and they are in a very, very strong position to deal with the problem they face.
"But of course it's a great void to fill for Manchester United, because the charisma and personality disappears suddenly in a club which has been dominated by it for such a long time.
"It's not an easy task to replace a person like that."