The 28-year-old stopper is at the top of Torino's list to become their new number one goalkeeper, per Sky Sports.
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But Leeds are reluctant to let the Brazilian leave the club this summer, with Karl Darlow having recently departed the club as a free agent to join Manchester United.
Perri was dropped for Darlow last season after a disappointing debut season for Leeds, having made 16 Premier League appearances.
Daniel Farke wants to bring in at least one goalkeeper this summer before allowing Perri to leave Elland Road.