The right-back is out of contract at the end of the season and the Gunners are fearful he may join a Premier League rival, with Manchester City, Chelsea and Liverpool all keen
The right-back is out of contract at the end of June, with the Gunners offering the Frenchman an €100,000-a-week two-year extension - with the option for a third year.
However, the club fear Sagna is ready to join a Premier League rival - with Manchester City, Chelsea and Liverpool all interested - and the 31-year-old has admitted a summer exit is likely.
"I'm out of contract, as everyone knows. I still consider myself as an Arsenal player at present," he told Europe1.
"But actually we had a small problem to agree [with the club], and I don't think I'll stay at Arsenal at the end of the season.
"It is a mixed season, we started very well, but we could have done better. Injuries have hurt us, especially those of [Aaron] Ramsey, [Theo] Walcott. At this level, it does not forgive."
Sagna is one of Arsenal's longest-serving players having joined from Auxerre in 2007.