Arsenal want the Barcelona midfielder, according to reports from Spain.
The 29-year-old's first season with the Spanish champions was mixed, following his £34 million switch from Atletico Madrid last summer.
The Turkey international was made to wait until January before even making debut due to Barcelona's transfer ban, and he later managed just 13 starts in all competitions.
His lack of game time might suggest that Turan could be unhappy in Catalunya and, according to Don Balon, Arsenal have tabled a bid for the talented midfielder.
The report goes on to claim that Barca would accept a 50 perent loss on their investment and sell him for £17 million, before noting that Galatasaray were ahead of Arsenal and Borussia Dortmund in the race to sign him.
Given his age, Arsenal boss Arsene Wenger may have reservations over moving for the 29-year-old.
But the French manager did, of course, trigger Jamie Vardy's Leicester City contract in what would have been a £20 million deal, and both players are the same age.
That being said, there is markedly less risk in going for Vardy by virtue of the fact that he is proven in the Premier League.