The 33-year-old, who featured for Cameroon at the World Cup, is without a club following his release from Stamford Bridge at the end of last season but could prolong his Premier League stay with the Hammers.
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The Cameroonian's high wage demands as well as the length of the contract on offer could prove a sticking point, although Goal understands talks are ongoing in the hope that a deal can be reached.
Eto'o is keen to stay in England after an up-and-down campaign with Jose Mourinho's side following his move from Russian outfit Anzhi Makhachkala back in August 2013.
The forward clashed with the Portuguese during his short spell at Stamford Bridge, with Eto'o having labelled Mourinho a "puppet" back in May after the Chelsea boss was caught on camera mocking the player's age.
With Mauro Zarate and Enner Valencia having already arrived this summer, West Ham are hoping to conclude a short-term agreement with Eto'o as they look to cope without Andy Carroll, who is likely to miss at least the first three months of the season through injury.