The Russian side are desperate to bring Champions League football to Dagestan within three years.
Sports Illustrated claims team director Roberto Carlos has been given the task of bringing top talent to the club.
Anzhi Makhachkala is owned by billionaire Suleyman Kerimov, who has funded several big-money signings since buying the club in 2011.
Chelsea striker Fernando Torres and Napoli forward Ezequiel Lavezzi are some of the players being linked with the Russian side.
