The Reds want to sign the former Chelsea man, who could potentially link up with Mario Balotelli at Anfield
Liverpool, which is on the verge of signing Mario Balotelli from AC Milan, is also ready to push through a deal for Eto'o as Brendan Rodgers looks to bolster his attacking options before the close of the transfer window.
Eto'o is a free agent after leaving Chelsea earlier this summer and has attracted the interest of a number of clubs in Europe, North America and the Middle East.
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It is understood the Cameroon international's preference is to remain in England and the Premier League after enjoying his one season at Chelsea last term.
Ajax and Everton have both expressed an interest in Eto'o, but it appears Liverpool is now in pole position to land the former Barcelona and Inter star.
Liverpool has offered Eto'o a one-year deal on 93,000 euros a week, with performance-related bonuses and the option of another year if he impresses at Anfield.
Should Eto'o and Balotelli join Liverpool it would see the two strikers link up for a second time after they played together at Inter.