The Cameroonian forward is currently without a club after being released by Chelsea earlier this summer.
Speculation over the course of the past few days has suggested that Liverpool are attempting to draft him in to bolster their attacking ranks, but now it has emerged that Everton are also in the running.
The Reds are reluctant to match the 33-year-old’s massive wage demands – around £135,000-per-week – to bring him in on a one-year deal, but more talks are scheduled.
But the Toffees may beat them to the punch, with Roberto Martinez interested.
His salary might also be a bridge too far for the Goodison Park side, but they have shown a willingness to splash the cash this summer by breaking their transfer record to land Romelu Lukaku in a £28m deal.
Eto’o is also understood to be wanted by West Ham and Tottenham, while foreign interest is strongest from Ajax.
The African star is said to have rejected lucrative deals to play in the Middle East in a bid to enjoy another season in England.