According to Diego Castro of Diario Gol (h/t Harry Howes of the Daily Star), Navas is unhappy with Real Madrid president Florentino Perez amid the club's reported interest in David De Gea and Thibaut Courtois, and Arsenal and Liverpool are monitoring his situation.
Both sides could use some fresh blood between the sticks, with Gunners goalkeeper Petr Cech now 35 and no longer the force he once was, while Loris Karius has failed to usurp Simon Mignolet at Anfield, and so the Reds are still on the lookout for an upgrade.
Navas has been Los Blancos' No. 1 since 2015 and has since made 109 appearances, keeping 38 clean sheets.
The Costa Rican is perhaps outside the conversation regarding the best goalkeeper in the world—for most that would likely be between De Gea, Courtois, Manuel Neuer, Jan Oblak, Gianluigi Buffon or Hugo Lloris—but if he is, it's only just.
As ESPN FC's Dermot Corrigan demonstrated, Navas' form dipped around March as he made some mistakes, but he regained it during the run-in to help Real win La Liga and the UEFA Champions League:
The 30-year-old has been strong this season, too, and he caught the eye when Real drew 1-1 with Tottenham Hotspur in the Champions League, per SB Nation's Lucas Navarrete:
He made two superb saves to deny Harry Kane, with the latter—in which he tipped a shot round the post during a one-on-one—drawing praise from La Liga writer Andrew Gaffney:
Indeed, Navas' reflexes and agility are among his best traits.
His distribution is strong, too. According to Squawka, he has maintained a 79 per cent distribution accuracy this term, higher than both Cech and Mignolet.
Should Real bring in another top 'keeper to replace him, it seems unlikely Navas would remain at the Santiago Bernabeu given he can be a No. 1 almost anywhere else.
He'd be a strong addition for either Premier League side, though it wouldn't be too surprising if they face competition for his signature.