Diario Gol, as quoted by TeamTalk.com, is reporting that the Gunners are interested in signing the Costa Rica international.
The same article states that Arsenal are interested in the 30-year-old to replace Cech, whose performances have been in decline.
According to the same story, the Gunners could face competition from Premier League rivals Liverpool for the shot stopper.
Navas has been forced to contend with regular speculation surrounding his future at Real Madrid since moving to The Bernabeu in 2014.
The Champions League holders have been regularly linked with a move to sign Manchester United goalkeeper David De Gea.
The Spain international was on the brink of a move to Old Trafford in 2015 before his proposed move fell through on La Liga’s deadline day.
Chelsea shot stopper Thibaut Courtois has also been linked with a move to the La Liga giants.
Arsenal have conceded 16 times in 11 games in the Premier League this season to raise serious questions about Cech.
The Gunners are in sixth place in the Premier League table behind Liverpool in fifth spot.
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