Samir Nasri, Andrey Arshavin, Gael Clichy, Johan Djourou, Tomas Rosicky and Lukasz Fabianski are all out of contract at the end of next season.
The Sunday Telegraph reports that Wenger is keen for the players to sign new deals in order to fend off interest from rivals clubs.
Nasri and Arshavin have been linked with both Barcelona and Inter Milan in recent weeks.
