Suarez joined Barcelona for around £75 million last month and Reds manager Brendan Rodgers has so far failed to find someone to take the Uruguayan's place in his squad for the new season.
The Northern Irishman tried to bring Queens Park Rangers striker Loic Remy to Anfield last month, but the plug was pulled at the 11th hour amid fears over the France international's medical results.
Rodgers has so far spent around £90 million on the likes of Adam Lallana, Dejan Lovren, Emre Can, Javier Manquillo, Lazar Markovic, Divock Origi and Rickie Lambert.
However, Lambert's arrival was completed before Suarez left for the La Liga giants, while Belgium international Origi will spend the coming campaign on loan at Lille.
Swansea City star Wilfried Bony has been linked in connection with the five-time European Cup winners, but they are understood to have been put off by the £19 million asking price from the Welsh club.
According to The Mirror, Liverpool have now turned their attention to Eto'o, who is a free agent after his one-year deal at Stamford Bridge expired in the close season.
The club are understood to have held talks with the Cameroon striker's representatives over a £40,000-a-week deal.
Eto'o has been the subject of reported interest from QPR and West Ham United, but the lure of playing in the Champions League again is likely to tilt Eto'o towards the Reds.
The move would represent something of a damp squib to Reds fans, who have seen their club talked about in connection with Radamel Falcao and Edinson Cavani in the last week.
The 33-year-old, who is also wanted by Ajax, is entering the twilight of his career and is not the same striker who terrorised defences across Europe with Barcelona from 2004-2009.
Eto'o was rotated with Fernando Torres by Jose Mourinho last season and the ex-Barca man made 21 appearances and scored nine times, including a hat-trick against Manchester United.
However, with just Lambert, Daniel Sturridge as their only recognised strikers and with the future of Fabio Borini still far from certain, Rodgers is acutely aware of his need to bolster his forward options following the loss of the 31-goal PFA and FWA Player of the Season Suarez.