Los Blancos have been alerted of the player’s potential a while back and they are ready to sign him at a cut-price in the summer.
The 18-year-old goalkeeper has a youth contract at San Mames and would be available for around €1 million in the summer transfer window.
Athletic Bilbao officials are eager to hold on to their prized asset, but talks over a new three-year contract have not progressed as planned.
Therefore, it appears that Kepa will ultimately decide to leave los Leones for a chance to join Real Madrid.
The talented keeper has yet to be handed a first team debut at San Mames, although he did make 5 appearances for Athletic B this season.
Kepa is currently a first choice shot-stopper for Spain Under-19, and has featured in six matches during the previous qualifying campaign.