The report claims, three clubs from MLS – Los Angeles Galaxy, DC United and Chivas USA are the expected landing destination for the Cameroonian.
Toronto FC have also showed interest, but the former Barcelona star reportedly has no interest in to join Canadian club.
If the striker move to MLS, then there is a scope of Romelu Lukaku to return at Stamford Bridge, as he continues with his impressive premier league performance at Everton (on loan).
Chelsea boss Jose Mourinho has already indicated that January signings are unlikely, he will make a couple of changes to bolster the squad for the next season, although he insisted that he is not going to change the squad anytime soon, instead play with the same players.
The four-time African player of the year, 32, whose current contract at Chelsea expires next summer. Eto scored two goals in seven appearances for the Blues so far in this term.
Chelsea to host Crystal Palace in Premier League action on Saturday 14 December, 15:00 GMT.
The Blues are currently sit in third place on 30 points, five points behind the premier league leaders Arsenal.