'Diario Gol' claim the Reds are 'very interested' in signing the Real Madrid stopper, who somehow still doesn't have the trust of club president Florentino Perez despite helping 'Los Blancos' to back-to-back Champions League titles and La Liga last season.
Navas may even be forced out of the Spanish capital with Real keeping a close eye on Manchester United's David de Gea and AC Milan's Gianluigi Donnarumma.
De Gea has consistently been linked with a move to the Bernabeu over the last few years, while Donnarumma was on the club's radar until he recently signed fresh terms with the Italian club.
Meanwhile, Navas will play no part in Real's crucial Champions League tie against Tottenham on Wednesday due to an abductor problem that has seen him miss the last three games.