The Holland international played under Wenger for eight seasons before leaving to join Premier League rivals United for a fee in the region of £24 million, and his ex-manager has praised Van Persie’s attributes.
Writing in his Eurosport column, Wenger said: “Robin van Persie is the kind of player you rarely meet in your life: an exception, the very definition of the word.
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“He has everything a coach dreams to have in a single player: he's smart, classy, clever when he moves, has killer-instinct, and is focused during 90 minutes.
“He spent eight seasons with me, and he never stopped developing himself. We could never imagine he would become the player he is right now. It hurts to see him wear another shirt when he is at top level.
“Now he's gone, don't ask the fans to understand what is not understandable. Even I do not understand, and I am deep at the heart of the decisions.
“You have to deal with it. That's life. We are here to help people to express their talents. A coach must have a positive influence on their players' lives.”
Italian giants Juventus were reportedly chasing Van Persie’s signature before he moved to Old Trafford and Wenger has admits he would have rather sold him abroad.
He added: "I would have preferred Van Persie to sign for a club in a foreign country, in order to avoid playing against him several times per season, but it's a fine challenge for us to prove we can exist after such a move, to show we can score goals, play well and survive everything."
Although he is pained by Van Persie's decision to move to Old Trafford, Wenger believes his former star striker can form a deadly strike partnership with Wayne Rooney.
“RVP and Wayne Rooney have everything to play together," he continued. "Sometimes, great goalscorers don't really fit together. But if you analyse the pair's technical skills on the pitch, it can work.
“It will require some understanding, from the technical and from the personal point of view, but their separate success will increase the links between them.
"If those links exist and if they both score, it will be very, very strong.”