Alves has been impressed by the 21-year-old midfielder and is keen for him to join Cesc Fabregas and Alex Song in leaving the Emirates Stadium for the Catalan club.
"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 [Andres] Iniesta," said Alves, quoted in the Daily Telegraph.
"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."
Alves lined up against Wilshere at Wembley in an international friendly earlier this month, with England emerging as 2-1 winners, but the right-back does not feel the defeat was too significant.
"England are a historic team which is not going through its finest period," Alves added. "But coming up against a rival like this is always difficult.
"Excuses are not valid in this sport but we had players from Brazil who haven't played much at all. Because of these circumstances, I think we did a good job. There were good and bad things."
Alves was speaking ahead of Barcelona's UEFA Champions League tie against AC Milan on Wednesday and the 29-year-old is expecting a tough game.
"They will be difficult opponents because of the tradition that they have in the competition," he said. "You have to show them respect.
"Milan is not experiencing its greatest period but these will be special games. We can't think about what Milan is going through, we just have to play our football and work hard because we know they are going to be tough games."