The 29-year-old has admitted that the North Londoners have been in touch but confessed that his future is unclear.
With the full-backs Nacho Monreal and Mathieu Debuchy having to fill-in at centre-half at times this season for Arsenal, the Gunners could surely benefit from signing an additional central defender this January.
The 29-year-old has been a star performer for Christiophe Galtier’s side this season, starting 11 Ligue 1 games in his role of captain of the club.
The defender, who been with Saint-Etienne for the entirety of his career, has revealed that the Gunners have been in touch but admitted that he is unsure of where his future lies.
"Frankly, I do not know,” Perrin told L’Equipe.
“There are always rumours, though Arsenal made inquiries and contacted my agent. But Saint-Etienne has always been most important, full stop.
"I have always said that the ASSE is my club and that if I go it would be to take the next step. When it comes to Arsenal, we are not talking about just any club.”
Arsene Wenger could call upon first-choice centre-half pairing Laurent Koscielny and Per Mertesacker in yesterday’s 3-0 victory over Stoke, but the French defender has suffered from injury this term and not been an ever-present.
Arsenal’s only major business in the transfer window thus far is to let Lukas Podolski leave to join Inter Milan on loan.