The Gunners desperately want to sign the 23-year-old centre-back.
Arsene Wenger's side are currently in the midst of a form slump, having lost their last three Premier League matches. Their defensive troubles haven't helped, and Wenger is looking to strengthen his backline.
And with Koscielny starting to show signs of ageing,El Gol Digitalclaim the Frenchman will be offered to Atleti.
Diego Simeone is believed to be a fan of Koscielny and could see him fitting into their system.
Gimenez has two-and-a-half years left on his current deal, but he is reportedly interested in making the switch to England.