The Cameroonian veteran is currently searching for a new club after being released by Chelsea, and is understood to be desperate to stay in England.
Liverpool have been mooted as frontrunners for the 33-year-old, even with Mario Balotelli’s immanent arrival.
Although talks have collapsed once between the club and the player, a fresh offer is expected from Anfield, however it may not be enough.
Everton are also in the hunt, and are so keen to get the ageing goal-getter in that they will present him with a two-year deal.
Liverpool – and all other interested sides – are thought to be only presenting 12 month contracts, which could make the security of another season at the highest level tempting for Eto’o.
It remains unclear as to whether or not his £100,000-per-week salary demands will be met, but Everton are hopeful that a deal can be reached.
The former Barcelona and Inter Milan star netted nine Premier League goals for Chelsea last season.