The Costa Rican international has become hot property this season due to some fine performances.
The Daily Mirror reports that Navas has attracted the attentions of Atletico Madrid, as well as Premier League duo Liverpool and Everton, who are all looking to bolster their goalkeeping ranks this summer.
The 27-year-old has helped La Liga minnows Levante keep 11 clean sheets in 27 games this term, a record comparable with the likes of Diego Lopez, Victor Valdes and Thibaut Courtois.
Navas is contracted to Levante until the summer of 2015, and despite preliminary contract talks back in October, the impressive shot-stopper has yet to put pen-to-paper – suggesting that a summer departure is likely.
Levante president Quico Catalan spoke to the Spanish press recently, however, and warned any potential suitors that the club would not be willing to sell Navas for any less than his reported €10m release clause.
Liverpool manager Brendan Rodgers only bought current Reds number one Simon Mignolet last summer, but with speculation also linking Liverpool with Barcelona's Victor Valdes, many feel that Rodgers wants another top goalkeeper who would push Mignolet and provide competition between the sticks as Liverpool look towards playing in the Champions League next season.
Everton, on the other hand face a bigger goalkeeping problem, as current number one Tim Howard, 35, is coming towards the end of his career. Everton manager Roberto Martinez will want to find a long-term replacement as quickly as possible.
But Liverpool and Everton will face stiff competition to sign Navas, with both AC Milan and Atletico Madrid thought to be interested in the the Costa Rican international.
Will Navas be playing Premier League football for Everton or Liverpool next season ?