Wilshere has established himself in Arsenal's midfield since he returned from a long-term ankle injury, and Alves has admitted that he would love to see the England midfielder at Camp Nou.
The Brazilian told reporters: "He is a great player who we have met playing against Arsenal and without doubt he can reach the height of the players we have here at Barcelona like Xavi and Iniesta.
"He has a lot of quality and a great personality. If I was given the chance to choose, he is a player that I would sign for Barcelona."
Wilshere has scored twice in 23 appearances for Arsenal this season.