The report states that a deal to sign Debuchy on a season-long loan is set to be completed in the coming days.
The France international made the move to Arsenal from Newcastle back in 2014 however, a series of injuries during his debut season at Arsenal allowed the youngster Hector Bellerin to take his spot in the side.
Debuchy was sent out on loan to the Ligue 1 side Bordeaux for the second-half of last season.
The reports from France follow Galatasaray sporting director Levent Nazifoglu confirming the transfer link.
“Mathieu Debuchy was offered to Galatasaray through his agent on a loan deal,” Nazifoglu was quoted as saying by Turkish-football.com.
Galatasaray are keen on strengthening their full-back position over the summer as head coach Jan Riekerink has not been impressed with Linnes and Sabri.
The 31-year-old has two goals in 27 caps for France since making his international debut back in 2011 but was ruled out of Euro 2016 with a hamstring injury.