Spurs are confident of completing a deal for the 25-year-old Anzhi Mahkachkala player in the coming days.
Willian has also attracted interest from Liverpool this summer.
The former Shakhtar Donetsk player would become the club's fifth major summer signing following the arrivals of Paulinho, Nacer Chadli, Roberto Soldado and Etienne Capoue.
If Spurs pull off the signing, it would be the third time this summer they have broken their transfer record.
In July, they signed Brazil midfielder Paulinho for a fee of just under £17m from Corinthians and earlier this month they spent £26m on Valencia's Spain striker Roberto Soldado.
Their previous high was the £16.5m paid for Darren Bent from Charlton in 2007.
Willian joined Anzhi in January for a reported £30m after five-and-a-half seasons at Ukrainian club Shakhtar Donetsk.
But the attacking midfielder has become available as Anzhi attempt to cut costs after a change in strategy by their owner.
This summer, Spurs have also signed 25-year-old French midfielder Etienne Capoue, 25, for £9m from Ligue 1 club Toulouse and Belgium international winger Nacer Chadli from Dutch club FC Twente for £7m.
The signings come amid continuing rumours about Gareth Bale's future at Spurs. The Wales forward, 24, has been ruled out of action for two weeks by a foot injury, but speculation continues that Real Madrid will make a formal £80m move.
Brazil attacking midfielder Willian has undergone a medical ahead of his proposed £30m move to Tottenham.