The France international has become a key player for Arsene Wenger's side since his move from Lorient in 2010, the vice-captain leading the first team in the absence of club skipper Per Mertesacker this past season.
The Gunners failed to qualify for the Champions League for the first time under Wenger after they could only muster a fifth-placed finish in the top flight, although they won a record 13th FA Cup title by defeating Premier League champions Chelsea in the final.
L'OM are believed to be interested in bringing Koscielny back to his homeland, and the 31-year-old centre-back has welcomed the rumours as he stopped short of committing his future to the north London giants.
"I have a contract with Arsenal, I even signed an extension last November until 2020. I feel very good over there," he told Telefoot.
"I have always said that I was a Marseille fan when I was younger. When a mythical club like Marseille contact you, it is good.
"But will I sign for them? I have no idea at all."