The west London side recently acquired Willian from Anzhi Makhachkala and now look set for another deal with the Russian team for Eto'o.
Recent reports have suggested the 32-year-old was weighing up a return to Inter Milan, but after appearing to be out of the race to sign Manchester United's Wayne Rooney, Chelsea have made their move for a new striker.
Four-time African Footballer of the Year Eto'o was an integral part of Mourinho's Champions League-winning Inter side in 2010, before heading to Anzhi the following year to become the highest-paid player in the world.
Anzhi are in the process of slashing their wage bill with owner Suleyman Kerimov desperate to balance the books of the financially-troubled club.
Sky sources understand that Eto'o will be officially revealed as a Chelsea player by Friday lunchtime.