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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.