The 25-year-old only moved to Dagestan in January but, following an indication from owner Suleiman Kerimov that costs would be cut severely, could be set to follow several players through the exit door, with long-time links to the Premier League renewed.
"For now, all there is are talks. I haven't received anything official yet," Willian told ESPN Brasil.
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"Now I'm waiting for a new bid to arrive in the next days from a few clubs, like Liverpool. If it's really Liverpool, then it is surely a great club. I'm hopeful and very calm, just waiting for the best."
"England is my goal. Of course the English championship is the dream of many players and I'm no different. I like the Premier League very much, I enjoy the English football and certainly, if that happens, it will be very good for me and for my image.
"All I know is that [Kerimov] told us that Anzhi wouldn't be making further investments, that in six months they will be returning to Makhachkala, that they'll be going home, that more Russian players will arrive and that, if the foreign players who had offers would be free to go, that he would help us.
"He doesn't want to let anyone go for free but he made it clear that, if good bids arrive - something at least close to what he paid for the players - he would certainly help us go. Not giving anyone away. If a good offer for the arrives, they'll let us go; if not, we stay. That's it."