Marca says Real expect to complete the signing of Kepa with an offer of â‚¬25 million being made as soon as the transfer window opens.
The Spanish goalkeeper's contract dispute with Athletic Club has been a longstanding issue, he has been in negotiations for over 12 months and an agreement hasn't been reached. His current deal expires in June.
With Los Blancos looking to plan for life after Keylor Navas, completing the signing of a hugely promising 23-year-old stopper with LaLiga experience is now viewed as a priority.
From January 1, Kepa will be committed to the European champions for the next six seasons on a contract that will pay him â‚¬2.5m as an annual salary.