The Anfield manager was frustrated in his attempts to bring QPR striker Loic Remy to the club earlier this month, and he still wants at least one more forward in before the September 2 deadline.
Liverpool need options
A number of big-names, including the likes of Radamel Falcao and Paris Saint Germain's Edinson Cavani, have been linked with the Merseyside club but Rodgers is preparing contingency plans.
He expects Falcao to end up at the Bernabeu, while Liverpool are not convinced Cavani is actually up for sale. In any case, they may not be able to afford his likely sizeable wage demands.
Which means Liverpool are preparing cut-price alternatives - and that's where Eto'o comes in according to the Daily Mail. The Cameroonian international is available on a free transfer after he was released by Chelsea at the end of the season.
He showed flashes of his old self at Stamford Bridge, but was not retained as Mourinho opted instead to bring in Diego Costa and Didier Drogba.
Champions League experience vital
But, while Eto'o does not fit the mould of a typical Rodgers signing, he does bring vital Champions League experience to the table. The three-time winner of the competition could be a savvy addition to a squad short of the know-how required to travel deep into the knock-out rounds.
Eto'o is no more than a name on a shortlist at the moment, but it's telling that Rodgers is considering all options available to him, even non-traditional targets, as he looks to bolster his squad ahead of a challenging campaign.
The signs are encouraging for Liverpool fans though, even without Luis Saurez. The Reds looked in magnificent form as they brushed Borussia Dortmund aside at Anfield on Sunday, with Coutinho in particular pulling the strings.
Liverpool face Southampton in their opening Premier League fixture next weekend.