Speaking to reporters while on holiday in his native Brazil, Cavalieri was quick to state if he was to leave Anfield, he would stay in his adopted continent.
He said: "Until now, no official proposal from the Corinthians came to me. But my idea is not now to return to Brazil.
"I am well adapted to European football and the only thing I think about is changing time to have more opportunity."
Asked where he would go if he made the transfer back home, he insisted he would only consider his former club: "If I return to Brazil, I'll be back to Palmeiras."