The Brazilian playmaker is available despite only joining Anzhi Makhachkala in January as their owner Suleiman Kerimov scales back his financial commitment to the Russian club.
The Reds were thought to be in pole position to land the 25-year-old, with Sky Bet initially considering them favourites until a shift is betting patterns on Sunday evening.
Anzhi are likely to expect to recoup a fee somewhere near the £30million they spent during the last transfer window, while Willian's wages are thought to be substantial.
Sky Bet Football Trader Chris Spicer said: "We were pretty much only laying bets on Liverpool after it became apparent that Willian would be available, but that has certainly changed.
"The money has continued to come for Spurs at as short as odds-on with punters seemingly expecting significant funds to be available as they also backed Bale to join Real Madrid at short odds."
Odds subject to change.