Real Madrid want Kepa to provide competition for current No 1 Keylor Navas.
The 23-year-old has a £17million release clause in his contract which Real will activate now to guarantee getting him.
Real could wait until the summer to sign him for nothing but know, in doing so, they risk missing out to a rival club.
Bilbao want to keep Kepa but he has decided not to sign a new deal, leaving Real free to move.
Kepa will officially be allowed to talk with other clubs on January 1, although his camp are already aware of Real's interest.
Preliminary discussions have been held but personal terms on what is expected to be a six-year contract have yet to be agreed.
Kepa will be the only arrival in January, according to AS, because the club remain confident in the current squad.
They are only moving for the Spanish keeper as he is a long-term target who has become available in the market.
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