The Anzhi Makhachkala playmaker is available for a fraction of the £32m his Russian club paid for his services earlier this year, and Tottenham and Manchester City have been linked.
But the report claims City are not interested in signing the 25-year-old attacker despite the bargain price.
Anzhi have confirmed plans to change their "transfer strategy". Having focussed on high profile signings, often for extravagant fees and on large wages, the Russian club now plan to curb their spending.
Part of this shift will see the club's highest earners depart this summer, with Willian and Samuel Eto'o thought to be available.
Tottenham boss Andre Villas-Boas is a long-term admirer of Willian, and tried to bring him to Chelsea before joining the north London side.
City have also been linked with him in the past, but Manuel Pellegrini has already completed the majority of his transfer business this summer.
The new manager has brought in Fernandinho - a former teammate of Willian from their days at Shakhtar Donetsk, Jesus Navas and Alvaro Negredo from Sevilla and Stevan Jovetic from Fiorentina.
Pellegrini has hinted at more signings before the transfer window closes, but it seems Willian will not be on their shortlist which provides a boost to Tottenham's pursuit of the Brazilian.
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