It was revealed on Tuesday that Anzhi is prepared to dip into their deep pockets to finance a big-money move for the Inter Milan striker.
And Inter has announced they are prepared to consider the offer put to them.
Anzhi now believe it has every chance of luring one of the most potent forwards in European football to Russia.
Eto'o's representative believes an agreement could be struck, with initial talks regarding a transfer having already been held.
Claudio Vigorelli told sports.ru: "We have almost reached an agreement with Anzhi. We now hope that the clubs can agree with each other."
While Inter has done little to rule out an imminent exit for their 30-year-old striker, owner Massimo Moratti insists there is no guarantee that a sale will be sanctioned.
He said: "At the moment Eto'o is not going anywhere and we are not negotiating for someone else to come in.
"We are only answering other teams that are interested in our players.
"I don't want to offend those who have made interesting offers for our players, offers that are right for the players' value.
"Then it will be up to us and the player to decide if we want to accept an offer or not.
"I have to say that, luckily, almost all of our players are sought-after."