The Daily Mail says he has been linked strongly with Bayern Munich, Paris Saint-Germain and Juventus, and will now talk things over with his agent, Pere Guardiola — the brother of incoming Bayern coach Pep — and his lawyers.
Liverpool insist they want Suarez to stay on Merseyside for the remaining four years of his contract.
But they may have to let the 26-year-old leave if he believes he has become a pariah and feels compelled to examine the alternatives.
Can Liverpool resist the offers and convince Suarez to stay? Should they? Give us your shout below...