Raul will be sold at a cut-price £5million at the end of the season says the newspaper.
Liverpool boss Rafael Benitez wants to strengthen his options up front for next season and is keen to bring in Raul in the summer.
A Madrid source revealed: “Real president Ramon Calderon is starting to think it is time to overhaul the squad and bring in younger and fresher players.”
Raul’s agent, Gines Carvajal, said: “If he leaves Real his destination would be easy to choose. It would be England.”