The Italy international has struggled to make an impact this season for Juventus and has yet to score a Serie A goal in the current campaign.
Amauri has been strongly linked with a winter transfer window switch, and his agent Ernesto Bronzetti told Sky Italia: "The truth is that we have said no to two English clubs - West Bromwich and Fulham."
He added: "These two clubs are not at his level.
"I don't think it would have been good for Amauri to join these teams because they are in the low positions in the standings.
"Moreover, it would have meant they would have had to adapt to a new life, with neither he or his wife speaking the language."
Amauri, 30, has been linked with a move to Serie A side Parma as well as a return to his former club Palermo.