The Dagestan-based giants beat the Premier League duo in the race for playmaker Willian last month, after convincing the Brazilian to reject a possible move to England
With the Russian transfer window not due to close until the February 24th, Anzhi are able to conclude a deal in the coming weeks, a luxury that English sides are without.
They are believed to be preparing a £12.8m bid, and are willing to offer him a lucrative deal to leave Italy.
Anzhi are openly searching for a top level centre-back after losing Christopher Samba to QPR last month, and are thought to see Benatia as the ideal replacement.
The 27-year-old is contracted until 2017, but a big money move may tempt his employers to part company with their star defender.
As well as Chelsea and Tottenham, AC Milan are thought to be interested in the Moroccan international, who has been impressive in Serie A this term.
Benatia started his career in France before some notable displays with Clermont led to a bid from Udinese in 2010.