Since the Magpies earned promotion back to the Premier League, boss Rafael Benitez has been searching for a goalkeeper with top-flight experience but the Spaniard missed out on Willy Caballero and Pepe Reina earlier this summer.
According to Tuttomercatoweb, Benitez has now turned his attention to Greek stopper Karnezis with the new campaign just two weeks away.
The 32-year-old has spent the last three seasons playing for Udinese, with 108 appearances being made in Serie A during that time.
Should any move be completed, Karnezis would face competition from the likes of Rob Elliot and Karl Darlow, who have both enjoyed spells between the sticks for the North-East outfit over the past two seasons.
Newcastle begin the new season with a home fixture against Tottenham Hotspur on Sunday, August 13.