La Stampa says Juve GM Beppe Marotta wants to cash in on the centre-forward to fund a bid for Fiorentina striker Alberto Gilardino.
Amauri is returning to full fitness and reluctant to leave Turin.
"I know if I am given my chance, I will prove myself here," he has confided to friends.
Juve have been in regular contact with Liverpool over Alberto Aquilani and their interest in Glen Johnson. Marotta is hoping Liverpool make a bid of around £8 million for Amauri, who would be a good foil for Fernando Torres in the Reds attack.