Eto'o is also wanted by Inter Milan, but the 32-year-old striker is set to shun their interest to secure a move to the Premier League with Chelsea.
It's understood that the opportunity to link up with former boss Jose Mourinho - whom Eto'o won the Champions League under in 2010 - is a significant factor behind the deal.
Having rejected the Italian giants' overtures, the powerful striker is looking to push through a Stamford Bridge switch this week ahead of the transfer deadline closing on September 2.
Eto'o has been offered a one-year deal with Chelsea, with the Blues seemingly confident of completing a £5 million move for the ex-Barcelona star this week.
Chelsea's pursuit of the world's most expensive player has been well documented in recent weeks, with Anzhi Makhachkala's owner looking to make drastic cutbacks, resulting in a number of their high-profile first-team regulars being put up for sale.
Eto'o's teammate Willian is another star set for Stamford Bridge, with Mourinho looking to conclude a deal for the samba star this week having agreed a fee in excess of £30 million.