The Bundesliga champions were keen on signing Kepa following the departure of Yann Sommer to Inter Milan.
However, Madrid came in at the last minute following an ACL injury to Thibaut Courtois, and will now take the Spaniard stopper on a one-year loan deal.
Dreesen has now claimed a deal for Kepa was very close.
“We were close to this deal and we actually wanted to present Kepa today. But he chose to join Real Madrid.
“He’s Spanish and so Kepa wanted to accept Real proposal,” Dreesen said.
