The France international has been one of the Gunners’ top performers this term, forming an impressive combination with Per Mertesacker at the rear of the Londoners’ XI.
His performances have been attracting admiring glances from Paris Saint-Germain, and now it appears that Real are also interested.
The Spanish giants are said to be looking to find a replacement for veteran defender Pepe, with manager Carlo Ancelotti thought to have lost faith in his abilities.
Koscielny is seen as the ideal partner for Sergio Ramos, thanks to his pace and ability on the ball.
Arsenal are unlikely to be open to the idea of letting one of their top performers go, yet the lure of challenging for trophies at the Bernabeu may be enough to sway the player.
The London club themselves are set to delve into the transfer market this summer, and their board are prepared to see stars leave to fund additions.