According to the Daily Mirror, the 24-year-old playmaker - who has been chased by Spurs and Chelsea in the past - has been transfer listed along with the rest of the Anzhi squad as the Russian club looks to undertake a "change in strategy".
Anzhi have previously pursued a policy of recruiting top class talent, sanctioning big wages to bring Samuel Eto'o to the club and splashing out £30m to sign Willian from Shakhtar Donetsk.
The Brazilian could be available for a cut price fee now though, as Anzhi look to offload their highest earners and bring in new faces on cheaper deals.
The report claims Lassana Diarra, Eto'o and Willian are three key players that face the chop.
Willian was strongly linked with a Premier League switch earlier this year, but he eventually opted to move to Russia in the January transfer window.
Expaining his decision, Willian said last week: "I had offers from big English clubs and other places, but Shakhtar never accepted them.
"I wanted very badly to go to England, but I have no regrets and couldn't wait any longer to leave Shakhtar - they used to tell me one thing and then act otherwise.
"Anzhi were the only ones who agreed to pay for my release clause. I have enormous affection and respect for this club, but everybody knows that my dreams and desires haven't changed."
Anzhi revealed their strategy reversal in a statement published on the club website, www.fc-anji.ru.
The statement read: "Having analysed the club's latest sports achievements following the results of the past period, Anzhi's administration has made a decision to work out the club's new and long-term development strategy.
"The new programme aims at gaining success in all the club's subdivisions with no time limitations.
"Changes to the club's budget are caused by the UEFA up-to-date requirements and linked with the club obligation to comply with Financial Fair Play but, at the same time, they won't lead to considerable deformations in the team's life and in the current structure of our club on the whole."
Spurs and Chelsea could now rekindle their interest in the talented playmaker, although there's likely to be no shortage of suitors in Europe.
Chelsea are well stocked in Willian's favoured position as well, with Oscar, Eden Hazard and Juan Mata.
Spurs also have strengthened in midfield, bringing in Paulinho while a move for France midfielder Etienne Capoue is also thought to be close.