Reds boss Rafael Benitez is impressed by Cole’s form and could make a move to strengthen his options up front in January.
Cole is reportedly a candidate for England boss Fabio Capello’s squad for the World Cup in South Africa next year.
Liverpool have also been linked with Valencia ace David Villa, Aston Villa forward Emile Heskey and AC Milan striker Klaas-Jan Huntelaar as Benitez atempt to bolster his attacking options.