The right-back's current deal at the Emirates Stadium expires in the summer, and he has failed to agree fresh terms.
The Mirror claims that he wants a three-year extension, while the Gunners have offered just a two-year deal.
Sagna has been linked with moves to the likes of Paris Saint-Germain and AS Monaco, although the report also suggests that Galatasaray have approached the player.
However, rumours which came to light last week said that he would stay in North London, with France Football stating that Sagna has been offered the three-year extension that he desires.
He has been with Arsene Wenger's side since 2007.