Goalkeeper Navas' stock has risen significantly off the back of a fine showing at the FIFA World Cup, in which he helped Costa Rica to the quarter-finals in Brazil.
Both Real and Bayern Munich have been linked with a move for the 27-year-old shot-stopper, who missed just one of Levante's La Liga games last season.
Navas has a €10 million release clause in his contract but, while Real appear keen to lure him to the Santiago Bernabeau, Catalan insists an agreement remains a way off.
"Madrid spoke with us and the deal is still not closed," Catalan is quoted as saying by AS.
"But certainly in the end Keylor will fulfill his dream."
Navas joined Levante in 2012 from Albacete following a loan spell with the Valencia-based club, but did not establish himself as a first-team regular until last term.
He was an integral part of Costa Rica's historic run to the last eight at the World Cup, conceding just two goals before Jorge Luis Pinto's men were beaten on penalties by the Netherlands.
