The 27-year-old winger has spent his entire career in Spain with Sevilla, but has been linked with a move away from the Ramon Sanchez Pizjuan Stadium at the end of the season.
Gunners boss Arsene Wenger has been credited with an interest in bringing the Spain international to the Emirates Stadium when the transfer window reopens on July 1.
However, Arsenal could now face serious competition for Navas's signature, after German newspaper Bild reported that Jurgen Klopp wants to lure the player to the Bundesliga.
Rated at around £17million, it's not yet clear if Wenger would be willing to part with that amount of cash needed to entice Navas to north London.
This year's Champions League finalists will have much deeper pockets this summer, though, after Bayern Munich activated Mario Gotze's release clause, agreeing a deal to sign the Borussia Dortmund midfielder ahead of the 2013/14 campaign.
Navas has been identified by the German club as a value-for-money replacement for Gotze, who cited a desire to play under Pep Guardiola at the Allianz Arena as the sole reason behind his move.