The Athletic Bilbao goalkeeper will join Zinedine Zidane’s side in the coming days.
Real Madrid will pay his £18m release clause and he will become back up to Keylor Navas.
Kiko Casilla is set to leave the club in January to make room.
And Cope claim that will be Real’s only piece of business this month despite the need for a striker.
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Real Madrid have been linked with Mauro Icardi, Harry Kane, Neymar and Kylian Mbappe.
But those deals are more likely to come in the summer when they are also hoping to sign a new first choice goalkeeper.
Madrid are already out of the running in La Liga as they trail Barcelona by a staggering 14 points during the winter break.
And they face a tall order in the Champions League having finished second in their group and with PSG to come in the second round.
And Zidane admits he’s held talks with the board over January deals.
"I talked with the president and we looked at everything," he said yesterday.
"We could speak about reinforcements, but there will be no signings at the minute, although anything could happen before the end of January.
"Of course, I don’t want any of the squad to leave."