The stopper has been one of the stars of his nation’s miraculous run to the World Cup quarter-finals, conceding just two goals in four games against Italy, Uruguay, England and Greece.
Both Liverpool and Arsenal have been alerted by his displays, with the Premier League pair both looking to draft in new ‘keepers this summer.
The Reds are set to let Pepe Reina join Napoli on loan for second successive campaign leaving them short of back-up to Simon Mignolet, while the Gunners are looking for a fresh face to replace FA Cup hero Lukasz Fabianski – who has joined Swansea on a free transfer.
Navas, 27, has a release clause of just £6.5m in his contract at Levante, and was being tipped to leave the coastal club prior to events in Brazil.
La Liga champions Atletico Madrid are also keen, but the lure of a larger salary in England may tempt the glovesman.
Navas has been one of the World Cup’s top goalies alongside Mexican Guillermo Ochoa – who is also wanted by Arsenal and Liverpool.