Regardless of whether Arsene Wenger remains with the Gunners, Arsenal are expected to make a number of major additions in the summer and that may involve an approach for centre-back Gimenez.
However, according to Gol Digital, Atletico boss Diego Simeone is only prepared to give the green light for the sale of a key player should he be able to sign a direct replacement.
The report claims that Simeone is an admirer of French international Koscielny, despite the player's indifferent form for much of the season.
Gimenez has previously insisted that he intends to see out his contract with Atletico - which runs until 2020 - and the Uruguayan has made a total of 26 appearances during the current campaign.
Koscielny also has just over two years remaining on his existing deal.