The report claims that the Gunners have expressed an interest in the Turkish international winger and that Barcelona are considering offering Turan as well as Munir and Sandro in a part-exchange deal for Mesut Ozil.
The Turkish international winger was closely linked with a move to the Premier League over the summer but ended up staying in Spain instead.
Turan joined Barcelona on a five-year deal from Atletico Madrid over the summer transfer window and Luis Enrique has lavished praise on the bearded winger after a bright start.
Barca may be reluctant to part ways with Turan after a bright start to his Barcelona career scoring twice and providing four assists in his first 17 games.
The reigning La Liga champions have won all but one of the games – drawing the other – Turan has featured in this season.
Turan would become the first Turkish international player to join Arsenal if he were to make the move.