The report claims that the Gunners are expected to join the race for the Barcelona midfielder who has been transfer listed.
The North London based club were closely linked with Turan last summer and his agent Ahmet Bulut confirmed he received official offers from Premier League sides.
“We had some great offers from the Premier League and we actually turned down the first bid made by Barcelona and it was only after they offered more attractive terms that we agreed,” Bulut was quoted as saying by the Fanatik.
Barcelona want at least £29 million for the bearded winger which is what they paid Atletico Madrid for him last summer.
Turan does have another four-years remaining on his current deal but the La Liga champions are ready to sell according to the latest reports from Spain.
Barcelona are considering letting Turan leave in order to recoup some of the transfer fee in the event that they manage to sign Andre Gomes from Valencia.
Turan is of course a former Lions player and remains a club legend. A move to Fenerbahce would be less likely considering they are the arch rivals of Galatasaray.
Borussia Dortmund are also reported to have made an enquiry for the Turkish international captain.
Turan missed the first half of last season due to the FIFA transfer ban imposed on the club but did make 15 appearances since making his debut in January.
Despite being linked with a move away from Barcelona, Turan has reiterated his desire to stay at the club next season.