The 27-year-old helped Costa Rica progress from a group that included England, Italy and Uruguay before his country fell in a penalty shootout to the Netherlands in the quarter-finals and was said to have agreed to join German giants, Bayern Munich, last week.
“Keylor at Madrid,” headlined the front page of the newspaper, which stated that Real Madrid had met Levante’s 10 million euro ($13.5m) release clause.
“Closed last week. Eight of the ten million clause is for Levante and 2 for the 27-year-old Costa Rican keeper,” the newspaper said.
According to Marca, the transaction will be sealed in the coming days, the time it takes to organise a transfer for keeper Diego Lopez to another club, possibly Napoli in the Serie A or French Ligue 1 side Monaco.
Navas was one of the sensations of the World Cup in Brazil, where Costa Rica made history by reaching the quarter-finals for the first time in its history.
He was voted man of the match in three of the five matches he played — England, Greece and the Netherlands.
Navas’s contract with Levante runs until June 2015