The Uruguayan ace is being linked with the Spanish club and says he would consider any offers that came his way as he ponders life beyond the critical English Premier League.
"I've worked hard since childhood to get where I am and I keep getting constant criticism from the English press. It makes me tired. Liverpool want me to stay, but do not know what will happen," he told homeland radio station Sport 890.
"It would be difficult to say 'no' to Real Madrid."
He added: "So far I have not received any official offer from Madrid."