Emanuele Giaccherini is expected to leave Sunderland after the Euros.
The Daily Star says Giaccherini, 31, wants a permanent move back to Italy after spending last season on loan at Bologna.
And Sunderland want to cash in before his contract runs out next year.
Torino are being linked with Giaccherini, which would mean a return to Turin for the former Juventus player.
Sunderland boss Sam Allardyce said: “I think the situation with Giaccherini is too far down the line.
“It was a situation at the club before I arrived, when he was already out on loan. If he came back now, we'd have to start discussing a new contract.
“We just hope he continues to have a good tournament as that could increase his valuation."