Reports claim the 30-year-old will become the world’s highest paid player if the move to Anzhi is completed.
Anzhi has agreed to pay between 20-30million euros for the highly-rated striker.
Eto’o will be handed a three-year deal reportedly worth 20million euros a year.
Anzhi representative German Tkachenko told ANSA news agency: “We are very close. We could close today, tomorrow or next week.”