It is understood City have no intention of making a move for the highly-rated 25-year-old, who is reportedly available as Anzhi slash their budget.
It is thought Willian, who only joined Anzhi in a £32million move from Ukrainian side Shakhtar Donetsk in January, could be available at a bargain price but that has not aroused City's interest.
Speculation linking Willian with City has arisen in Brazil after it emerged Anzhi intend to cut costs, ending their free-spending days of recent years.
Star striker Samuel Eto'o is reportedly another top earner the club are willing to offload.
City have already signed four new players this summer in Fernandinho, Jesus Navas, Alvaro Negredo and Stevan Jovetic for a combined cost of nearly £90million.
Manuel Pellegrini has also suggested there may be further new arrivals before the close of the transfer window but it is understood Willian will not be one of them.
Meanwhile captain Vincent Kompany is optimistic ahead of the new season and says nothing should be read into Saturday's friendly loss to Arsenal in Helsinki.
Kompany says the squad worked particularly hard in their last full week of training together before they begin their Barclays Premier League campaign.
Kompany told City TV: "The result is not that important.
"If it wasn't good enough, I would say it, but we did an incredible amount of work, and the game was just to top up the physical work we have done.
"I know both teams had different kind of work in the lead-up to the game.
"From the information I have got, their build-up was completely different, so we are happy with what we have got out of the game."
City's squad has now dispersed for internationals but they begin their season against Newcastle at the Etihad Stadium next Monday.