Vagnati admits the striker's contract status means he could be moved on.
"I hope he can remain as long as possible," Vagnati told Sport Mediaset.
“His contract expires in 2022, but there's still time to talk. You never know in football, anything can happen, but we hope that he stays with us.
“Andrea cares a great deal about Torino and that is a very important element. We'll see what happens in future."
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