The 30-year-old has one year left on his current contract and hasn't been offered a new deal at the Emirates Stadium.
Sagna is unlikely to be offered a long-term deal as Arsene Wenger has a policy of only allowing players over 30 to remain on short-term deals, and his representative, Christophe Mongai, has left the door open for an exit.
"This is not the best time to talk about Bacary's future," Mongai told Russian newspaper Izvestia. "He's contracted to Arsenal and the season is still not over. We'll see what happens in the summer."
Russian giant Anzhi Makhachkala, along with cash-rich French duo Paris Saint-Germain and Monaco, have been linked with a move for the right back.
The Frenchman arrived at Arsenal from Auxerre in 2007 for an undisclosed fee.