The Cameroon striker has been made an offer by Roberto Martinez's team after city rival Liverpool pulled out of a bid to take him to Anfield on a short-term deal.
Samuel Eto'o is closing in on a free transfer to Everton after Liverpool pulled out of a deal to sign him, Goal UK reports.
Roberto Martinez's team has made an offer to the 33-year-old striker and is hopeful of agreeing to terms. Eto'o was in line for a move to Liverpool until Brendan Rodgers switched his attention to Mario Balotelli, who is expected to complete a 20 million euro switch to Anfield on Monday.
Martinez wants to sign an additional striker to provide proven backup to Romelu Lukaku, with Manchester United's Danny Welbeck also being monitored.
Eto'o wants a two-year deal and is likely to lower his wage demands of 163,000 euros a week if a contract with a Premier League club is spread over a longer term.
Asked about speculation linking Everton with Eto'o and Welbeck, Martinez said: "There is a lot of money involved in those two. At the moment, if I am honest with you, I am looking at all the options.
"While the window is open we are looking at anyone who can help us and also looking at our injured players and seeing how they react. Bryan Oviedo and Arouna Kone will have a big say on how we end the window and I have an open mind about it. We are to going to make sure we make the right decisions."
Cameroon star Eto'o was released by Chelsea at the end of last season and is currently a free agent.