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.
Their more significant concern is over the Nasri situation.
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.
The France international scored 15 goals in 45 games last season and was the outstanding performer for Wenger's side in the first half of the campaign.
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.
The prospect of losing the two players will only heighten the concerns of Arsenal fans. Barcelona are again being linked with inspirational skipper Fabregas and, in addition, Manchester United-bound Phil Jones turned down a move to the Emirates from Blackburn.
Wenger has signed the 19-year-old defender Carl Jenkinson from Charlton and been heavily linked with promising Southampton winger Alex Oxlade-Chamberlain but those arrivals are unlikely to appease disgruntled fans.