Dutch sports website Voetbal International broke the news Friday.
During his tenure as manager of the national team from 2006 to 2010, Hiddink led Russia to the semifinals in the 2008 European championships. He left after the team failed to make the 2010 World Cup.
Kerimov, a native of Dagestan, has poured money into the club since buying it last year, acquiring big-name talent like Roberto Carlos, who led the Brazilian national team to a World Cup title, and Cameroonian striker Samuel Eto'o, considered one of the world's best players. Eto'o earns more than 10 million euros a season with Anzhi.
The billionaire owner, a financial investor thought to have close ties to the Kremlin, has also spent 100 million euros on a new stadium for the club and plans to fork out another 600 million euros for a second arena that can hold 45,000 spectators.