Reds boss Benitez had a £3million bid for the Israeli winger knocked back earlier in June - and is reportedly prepared to return with an improved offer of £4.5million.
The Hammers have pulled the plug on a new contract offer for Benayoun after he expressed his desire to move to the Champions League finalists.
However, Liverpool's initial bid was deemed unacceptable by the Hammers, so they will come back with a fresh approach.
Benayoun said: "I'm honoured a club like Liverpool is interested in me. I'm contracted to West Ham, so we will have to see what happens."
According to The Sun, Benitez is willing to use Welsh striker and reported Hammers target Craig Bellamy in a swap deal for Benayoun.
The Irons are keen to strengthen their forward line after Charlton hitman Darren Bent rejected a move to Upton Park.
Therefore, Bellamy could be an ideal makeweight in the deal, after Benitez made it clear that he is surplus to requirements at Anfield.
Vi bruger cookies for at kunne give dig den bedste oplevelse. Ved at bruge vores side accepterer du brugen af cookies. Du kan læse mere i vores persondatapolitik.