Wenger is available after leaving Arsenal as manager at the end of last season.
Villeneuve told Paris United: "Wenger in the management team? It would be great, because he is an outstanding manager, and always of a calm nature in the exchanges with the international clubs of first rank.
"Two clubs have always wanted him as a coach at one time. Bayern, after Monaco, absolutely wanted him since he is quadrilingual, and I attended a fitness centre in Italy for the negotiations of Real Madrid with him. And he stayed at Arsenal.
"The dimension that he would render a great service, but not as president. President Nasser fulfills his duties very well, but they must also say that a great club is also great leaders
"Not just great players. So yes, I long for him to come to PSG. The Parisian leaders have wanted Arsene Wenger a lot at one time, but he never wanted them. He's a monogamous one. His club, finally, was Arsenal."