The centre-back joined Arsenal from Lorient in 2010, and has made more than 300 appearances for the Gunners during his time in the English capital.
The 32-year-old is currently on the sidelines following Achilles surgery, but could be available towards the end of 2018.
Koscielny has admitted that he is thinking about "moving on" from Arsenal at the end of the 2019-20 season.
"I'm under contract until June 2020. Afterwards? I'm thinking of moving on, but I do not know where," Koscielny told Nice-Matin. "This is not relevant anyway! I am in England, my family too. Then there will inevitably be a lot of question marks.
"The bottom line is to have health. I learned to relativise because there are so many more serious things in life."
Koscielny has won two FA Cups and two Community Shields during his time with Arsenal.