Wenger has been an admirer of Turan since his days at Galatasaray but has never had the opportunity to work with the Turkish intentional.
Per the source, Barcelona would consider offers of £20 million for the bearded midfielder.
Turan missed the first half of last season due to the FIFA transfer ban on the club imposed on the club but his position may be in doubt after re-signing of Denis Suarez from Villarreal.
Turan is reported to be happy at Barcelona according to his agent Ahmet Bulut however, he has hinted in the past that he would like to play in the Premier League one day.
The 29-year-old was also looking for a flat in London last summer although that was before he joined Barcelona on a five-year deal.
Bulut has however, recently hinted that he cannot rule out a move this summer.
The agent told Calcio Mercato: “I know nothing of Milan’s interest in Arda. At the moment I can only say that he wants to remain with Barcelona. I don’t know, however, what could happen during the transfer window.”
Turan has had his summer break cut short and is currently the only player in the squad who featured in Euro 2016 that has been called back to pre-season training.
The experienced midfielder is under an intensive training program to ensure he is match fit in time for the start of the season.