According to talkSPORT, Milan's head coach Clarence Seedorf is keen to lure the 27-year-old Costa Rican to the San Siro to revitalise his squad and add competition to aging stopper Christian Abbiati.
Abbiati is now 36 years old and his best years could be over.
The in-demand keeper has a release-clause fee of around £8 million but is under contract until June 2015, per talkSPORT.
He has been in excellent form this season in La Liga, achieving 12 clean sheets in 25 appearances, per Squawka.
Navas' reputation has exploded this year, and it is likely more suitors will enter the race for him by the time the World Cup comes around.
Editor of Goal USA Jon Arnold recently tweeted about Navas and the interest he has caused:
Navas will be between the sticks for Costa Rica in Brazil during the summer, who play England in Group D.
First choice Liverpool goalkeeper Simon Mignolet is in his first season at Anfield, and though he has been impressive on occasions, he has looked vulnerable at other times.
Navas would give the 26-year-old signing from Sunderland huge competition for a starting berth, should he decide to move to Merseyside.
Liverpool have had a fantastic season this year and have been scoring freely, with the attack of Luis Suarez and Daniel Sturridge paying out dividends. But they have looked shaky in defence, and this has been in part to having a new goalkeeper.
To purchase Navas would put this process back to square one.
Mignolet has not been perfect in his opening gambit at the club, but the pressure is huge at the top end of the Premier League, and he deserves time to settle.
Navas is one of the hot new goalkeepers in Europe, and the buzz about him is building by the game. But it was only 12 months ago that you could say the same for Mignolet at Sunderland, when he was putting in great performance after great performance.
Brendan Rodgers should, and will, keep faith in the 26-year-old Belgian. Buying another goalkeeper of the standing of Navas could wreck Mignolet's confidence rather than improve competition.
We had started the game really well, went in front and arguably we should’ve been two up. Away from home there are critical moments in games and he had made that save going the wrong way. And that’s what he is, a brilliant shot stopper and I thought the back four, goalkeeper and collectively in front of that, we were excellent defensively.
Despite Rodgers' words, what is important is that the Anfield club purchase in defence.
They need one or two world-class players in front of Mignolet to organise and protect.
If they can do this, and retain Suarez and Sturridge, Liverpool will not just be competing domestically for the title in 2014/15, but will also be a credible threat in the Champions League.