The Levante goalkeeper, who starred in the World Cup for Costa Rica, looks set to join the Santiago Bernabeu side after they caved on their Liga rivals' demands
The capital club initially valued Navas at around €8m (£6.3m) but were told last week that they would have to match the player's minimum fee release clause if they wanted to prise the highly-rated shot stopper from the Valencia-based team.
The Spanish giants have responded by agreeing to pay the €10m required to acquire the services of the 27-year-old, who was regarded as one of the best goalkeepers at the World Cup as Costa Rica made it to the quarter-finals of the tournament before losing on penalties to Netherlands.
Levante, who finished 10th in La Liga last season, must offload the goalkeeper soon before they lose him for free with his contract expiring in June 2015.
The club are already set to announce Navas' replacement, as they are close to signing 24-year-old Diego Marino from Real Valladolid.