The 33-year-old is a free agent following his release from Chelsea at the end of last season and was strongly linked with a move to Merseyside rivals Liverpool this summer, as well as fellow Premier League sides West Ham and Sunderland.
It was thought Eto’o was close to signing for the Reds, though they instead opted to sign £16million striker Mario Balotelli from AC Milan.
Upon his release from Stamford Bridge, the Cameroon international insisted he wanted to continue playing in the Champions League, with Serie A runners-up Roma one of a host of other European sides linked with a swoop.
But it now seems Everton, who can offer the striker Europa League football this season, are leading the race to agree terms with the former Real Madrid, Barcelona and Inter Milan ace, whose career club tally exceeds well over 300 goals.
The Blues held detailed negotiations with the forward last week but after those initial discussions the chances of a move to Merseyside appeared to cool.
However, talks have re-started over a potential two-year deal as manager Roberto Martinez searches for an understudy to record signing Romelu Lukaku, with current back-up forward Arouna Kone still to return from a knee injury sustained in October.
Eto’o represents a wise buy for the Toffees boss, with the Spaniard surely hoping the experienced striker will have a positive impact on Lukaku’s progression following the Belgian's £28m permanent switch to Goodison Park.