The 29-year-old Frenchman only signed a new deal with the Gunners last summer.
But it seems he could follow Nacho Monreal out of the Emirates exit door.
The Daily Star claim Real Madrid are poised to announce Rafa Benitez as Carlo Ancelotti's successor.
And it is thought Koscielny is already on Benitez's wishlist should he be handed the job.
GETTY
Laurent Koscielny (right) is being lined up with a move to Real Madrid
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Monreal meanwhile, has been linked with moves to Atletico Madrid and Athletic Bilbao.
Koscielny's side lifted the FA Cup for the 12th time after their 4-0 win over Aston Villa at Wembley.