The Cameroonian ace has impressed while with the Hammers, whom he joined on a loan deal from Barcelona over the summer, leading to suggestions that the Irons and Manchester United are keen on mounting raids for him.
But, Liverpool chief Brendan Rodgers is keen to beat the pair to the holding midfielder, with Steven Gerrard’s impending exit set to weaken his central options.
Song himself is understood to be preparing to leave Barca permanently when his season at West Ham ends, with a full Premier League return his aim.
The east Londoners are keen to match the Spaniards’ valuation of their man, but Liverpool are hopeful that the chance to play for one of the nation’s biggest club sides may sway the African ace.
Manchester United are also interested.
Song endured two difficult seasons at the Nou Camp after joining the Catalan side from Arsenal.