"The signing of the deal will likely take place on Monday or Tuesday at the latest, as long as Samuel successfully completes his medical," Eto'o's agent, Claudio Vigorelli, was quoted as saying on Sunday.
Reports said that Anzhi will pay Inter 25 million euros ($36m) plus performance-related bonuses for the Cameroon skipper.
According to media rumours, Eto'o will receive around 20.5 million euros a year in wages, making him the world's top-earning footballer.
Meanwhile, Cameroonian defender Benoit Angbva, who currently plays for Anzhi, said he was the man who had initiated Eto'o's transfer to the club.
"We talked with Samuel in June, just before the friendly match between Russia and Cameroon," Angbva told daily newspaper Sport Express.
"He sent a message to the Dagestan club with me, saying: 'If Anzhi are ready to buy me, I will come.'
"I told him everything about the club, the training base, the players and the team's future prospects.
"Samuel believed me and later talked to the club owner, Suleiman Kerimov. In short, it was me who initiated this transfer."
Eto'o, 30, is the most decorated player in African history, having won the Champions League three times—twice with Barcelona and once with Inter.
The four-time African player of the year also won three league titles with Barca and one with Inter, while with Cameroon he has twice won the Africa Cup of Nations.
He began his career with Real Madrid before loan spells with Leganes, Espanyol and Real Mallorca, who he then joined permanently.
He helped Mallorca to a Copa del Rey victory in 2003, earning a move to Barca the next year.
He joined Inter in 2009 in a swap deal involving Zlatan Ibrahimovic, with the Italians also receiving 50 million euros.
Reports said that Kerimov, who is not only a billionaire but also a Russian senator, was also targeting Brazilian international defender Dani Alves, who is currently playing with European giants Barcelona.
Local media claimed Anzhi would have to pay between 35 and 40 million euros for the right-back.
Anzhi have only had one full season back in the Russian top flight but they have become major players since they were bought by Kerimov, who has poured money into the club.
Despite the dangers in Dagestan, where a low-level Islamic insurgency has made the republic very unstable, Anzhi have already managed to attract players such as Roberto Carlos and Yuri Zhirkov.
They play their home matches in Makhachkala but the players live and train in Moscow for security reasons.