The Romanian stopper is a free agent this summer after being released by champions Manchester City.
But Black Cats boss Gus Poyet has identified the 27-year-old as the perfect candidate to provide stiff competition for Vito Mannone at the Stadium of Light.
Pantilimon made just seven Premier League appearances for City last season and has had to play second fiddle to Joe Hart for a number of years at the Etihad.
But Crystal Palace’s Julian Speroni, who will also be a free agent this summer, is another goalkeeper catching Poyet’s attention.
Speroni, 35, was one of Palace’s star performers last season as they capped a successful first season back in the Premier League with an 11th place finish.
But a new Selhurst Park contract is yet to be agreed and Poyet could offer his fellow countryman a new challenge at Sunderland.
With Poyet desperate to replace the outgoing Oscar Ustari, following his decision to leave the club after just six months, Speroni could prove to be the more realistic target, with Mannone expected to remain first choice and Pantilimon eager for regular first-team football.