The Brazil international only joined Anzhi Makhachkala in a £32million deal from Ukrainian side Shakhtar Donetsk in January.
Anzhi Makhachkala are looking to cut costs and are ready to sell the winger before the transfer window closes.
Tottenham have long been linked with a move for Willian, but they now face competition from Liverpool.
Liverpool boss Brendan Rodgers is keen to make a marquee signing this summer and the 25-year-old former Corinthians star would fit the bill.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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