The 27-year-old goalkeeper helped his nation to the showpiece game in Brazil earlier this summer, impressing with his shot-stopping abilities and command of his area.
Brendan Rodgers is understood to have been alerted, and the Merseysiders have approached the Italian side to discuss a £2m deal.
Romero spent last season on loan at Monaco and has since been told that he can leave for the right price.
Rodgers sees him as a good back-up option for No. 1 Simon Mignolet, with space available following Pepe Reina’s switch to Bayern Munich.
Sampdoria are looking for a quick sale, but the Premier League runners-up may attempt to push a loan deal with a view to a permanent transfer to properly assess the stopper.
Reports suggest the Anfield side have been looking at David Marshall and Karl Darlow, but neither were suitable.
Romero made his name in Europe with AZ Alkmaar in Holland before joining Sampdoria in 2011.