The 31-year-old has been a mainstay of the Gunners backline since his £10.6m switch from Lorient in 2010, making close to 300 appearances for the club.
However, it is said that he is open to leaving the Emirates Stadium as he is tired of Arsenal's failure to mount consistent challenges for the Premier League title.
According to French TV programme Telefoot, the centre-back is high on the list of Marseille, who are determined to sign high-profile France internationals.
Meanwhile, The Sun believes that Pep Guardiola is eager to bring Koscielny to the Etihad Stadium as he looks to strengthen the Man City defence in the summer.
Koscielny only penned a new Arsenal contract in January this year, which tied him to the club until 2020.