The goalkeeper initially appeared to be on his way to Bayern Munich after Levante vice-president Tomas Perez claimed that a transfer to the Bundesliga champions was all but done.
Nevertheless, Navas has made it clear that he would prefer a move to the Santiago Bernabeu side after Madrid also agreed to meet his £8 million buyout clause.
"Real Madrid are my priority. Everything else gets put on hold for Madrid," the 27-year-old was quoted as saying by Marca.
Navas was one of the revelations of the 2013-14 La Liga campaign as he helped Levante to a 10th-place finish with a string of fine performances.
The former Saprissa and Albacete man further impressed at the World Cup, guiding Costa Rica to the quarter-finals, and he now seems destined to continue his career at Madrid.