On Thursday, it was claimed that Marseille were looking to sign the out-of-favour defender on a free transfer, but it appears that they will face competition to get a deal over the line.
According to reports in Turkey, Besiktas are ready to offer the full-back a lucrative contract in a bid to tempt him away from a return to France.
Despite signing for Arsenal three years ago, Debuchy has made just 23 appearances in all competitions, with his last outing coming against Bournemouth on November 27.
The Gunners are likely to bide their time before parting ways with the 32-year-old in a bid to receive a fee for his signature, but it appears inevitable that they will free up space on their wage bill with the exit of the former Newcastle United man.
Earlier on Friday, Arsenal announced that they had allowed Gabriel Paulista to sign for Valencia.