Goal understands that Stuani, 32, has emerged as a transfer target for leaders Barca.
With Munir El Haddadi completing a move to Sevilla last week, Barcelona have been left thin at the striker position.
But Stuani has now emerged as the club's leading target.
With 12 league goals this season, Stuani's La Liga tally is the best return from a player outside of Barca pair Lionel Messi (17) and Luis Suarez (14).
And Barca have focused in on the Uruguayan, who the club believe can be convinced to move to Camp Nou despite the likelihood of him earning less playing time than he currently enjoys at Girona.
Quizzed about a looming switch to Camp Nou, Stuani – who reportedly has a €15 million (£13m/$17m) release clause – told reporters: "I can't say anything."