The cash-laden Russians had been strongly linked with the Ivory Coast defender towards the end of the English transfer window and the threat of losing him remains at large
Toure, who is currently away on international duty at the Africa Cup of Nations, was suspended for six months of last season for the use of a banned substance but had begun to find form once again prior to his departure.
The Mirror understand the Russian side made an approach for the experienced defender but Mancini is believed to be unsure about letting him leave with City’s defence being surprisingly porous recently, picking up just one clean sheet in their last seven.
Anzhi are thought to be extremely determined to strengthen their defensive line after missing out on Paris Saint-Germain signing Alex and following a seventh place finish in the Russian Premier League.
Before heading to Equatorial Guinea and Gabon, Toure had formed part of the team that won five out of six matches, managing clean sheets against Liverpool and Arsenal, while Ivory Coast are yet to concede a goal at the tournament.
It is believed that the billionaire-owned side have made a very lucrative offer to Toure and it is also claimed they have offered City a large loan fee as they look to make the deal worth City’s while.