The Reds have identified him as a possible target to solve their striker shortage.
Eto'o, 33, is a free agent after leaving Chelsea at the end of the season.
The Cameroon international spent just one season at Stamford Bridge and netted nine goals.
He has played for Barcelona, Real Madrid and Inter Milan and has won four league titles and three Champions League crowns during his long career.
Kop boss Brendan Rodgers is keen to add further strike power after Luis Suarez joined Barcelona.
At the moment he faces going into the new season with just Daniel Sturridge, Rickie Lambert and the unwanted Fabio Borini as his only real options up front.
The Reds have already suffered a series of frustrations this summer in their hunt for more firepower.
They missed out on QPR striker Loic Remy after he failed a medical and were put off making a move for Monaco star Radamel Falcao because of his desire to join Real Madrid.
Rodgers also made enquiries about PSG striker Edinson Cavani but his £300,000 wages ruled out any possible deal.
Liverpool have yet to make a formal approach for Eto'o, and he would need time to get fit after missing pre-season
But Rodgers is anxious to get more cover in up front to build on last season's progress.
