That's according to the Daily Star, who carry reports from Italy that claim Liverpool are now in pole position to land the 33-year-old forward after Anfield officials held preliminary talks with Eto'o's agent on Tuesday morning.
Reports earlier yesterday had claimed that Brendan Rodgers had added Eto'o to his transfer shortlist having become frustrated in his pursuit of a new forward.
The Liverpool boss thought he had a deal for Loic Remy lined up, but a complication with the Frenchman's medical scuppered the deal. As a result, Rodgers has been left with just three weeks to strengthen his frontline ahead of the new season.
Italian journalist Fabrizio Romano first reported the Eto'o meeting. He said on Twitter: "Samuel Eto'o agent had a meeting with Liverpool this morning. #LFC made an offer; no agreement right now. New meeting is coming on next days."
Romano goes on to say that Everton have also had meetings scheduled with the same representative this week as interest mounts in the free agent.
Eto'o hit just nine goals for Chelsea in his single season at Stamford Bridge, and along with Demba Ba, was let go at the end of the season. Mourinho opted instead to bring in Didier Drogba and Diego Costa.
He publicly blamed his strikers on more than one occasion last season for costing his side points - their profligacy in front of goal was apparently the only thing letting Chelsea down in the title run-in.
Champions League experience
But Liverpool see Eto'o as potentially a valuable addition to their squad ahead of a Champions League campaign next season. Arsenal, Everton, West Ham and Tottenham have also been linked, with the Gunners and Toffees in particular thought to be looking for one more striker.
The three-time winner of the competition would lend his experience to an otherwise green squad, although it's fair to say he would not be the signing many Liverpool fans expected when they sold Luis Suarez to Barcelona.