According to Charles Watts of Goal, the French centre-back is set to have "his wish granted of securing a return to his homeland."
Koscielny refused to travel on Arsenal's pre-season tour of the United States last month in an attempt to force a free transfer away from the Emirates Stadium.
Gunners head coach Unai Emery subsequently said he was "trying to convince him to stay with us," per Sam Lovett of The Independent.
But the 33-year-old now looks set to exit the club after nine seasons in north London.
Given Koscielny has one year remaining on his Arsenal deal, the Gunners were never likely to let him go for free.
It will be some consolation they have managed to negotiate a fee for the former France international, but he will be a big loss nonetheless.
Arsenal are lacking in defence. They conceded 51 Premier League goals last term for the second season running.
Before 2017-18, they had not conceded more than 50 goals in a league campaign since 1983–84:
Koscielny, though, has remained consistent. His departure will leave Arsenal having to rely on the likes of Rob Holding, Sokratis Papastathopoulos and Shkodran Mustafi in the centre of defence.
That is a concern for Arsenal as none of the three are reliable, and they may well need to sign a new centre-back to replace Koscielny in the final days of the transfer window.