The 33-year-old had attracted interest from Everton, but is excited by the prospect of working under Brendan Rodgers.
Everton's late interest in the 33-year-old had threatened to derail Liverpool's move, with Roberto Martinez's side ready to offer a two-year contract, but the striker is excited by the prospect of working under Brendan Rodgers.
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The Cameroon international's medical is taking place outside of the UK, while the deal could be finalized before Liverpool faces Manchester City on Monday evening.
Eto'o is available on a free transfer having left Chelsea at the end of last season and had held talks with Ajax earlier this summer before the Dutch club pulled out of negotiations.
Eto'o scored 12 goals in 34 appearances for Chelsea last season but hit out at Jose Mourinho after the 51-year-old joked about not knowing the striker’s real age.
Liverpool is also poised to complete the signing of Mario Balotelli in a 20 million euro deal from AC Milan.
The Italy international has said goodbye to his teammates at the Serie A club and has traveled to England for a medical.