Arsenal fear that midfielder Samir Nasri and left-back Gael Clichy could leave the club this summer.
The pair have only a year left on their deals and Nasri, 23, has been linked with Manchester United, while Clichy, 25, is a rumoured target for Liverpool.
But the Gunners, who could also face a fight to keep Cesc Fabregas, stress that the door is open for Nasri and Clichy to negotiate new deals.
After a sixth season without a trophy, Arsenal manager Arsene Wenger is expected to strengthen his squad this summer.
He is likely to make one signing from France but that it is unlikely to be Belgian midfielder Eden Hazard, who has been linked with the club.
BBC Sport understands Arsenal are working on a deal for Hazard's Lille team-mate, Ivory Coast forward Gervinho, but reports that it could be completed this weekend appear wide of the mark as the clubs are struggling to agree a fee.
However, Wenger's hopes of ending the club's trophy drought will be dealt a blow if he loses both Nasri and Clichy.
Nasri signed for the Gunners in July 2008 from Marseille and has publicly stated his uncertainty over his Arsenal future, while not ruling out a move to Manchester United.
Clichy has been at Arsenal since the summer of 2003 and, even though he is one of the club's longest-serving players, the impact of his exit could be limited with Kieran Gibbs a ready replacement.
Source: The Punch