Chelsea have been told by Shakhtar Donetsk that only a bid of £24m or more will tempt the Ukrainian side into selling Willian, according to the Daily Star.
The Stamford Bridge outfit had a £16.7m offer turned down in January, but the Blues are expected to rekindle their interest in the attacker this summer as they seek to freshen up their squad.
The 23-year-old has had an extremely successful spell in Ukraine, winning three Premier League winners' medals and a UEFA Cup since signing from Corinthians in 2007.
His profile in England is set to rise this year when he appears for Brazil in this summer's 2012 London Olympics. Chelsea may want to seal the deal before the tournament, during which time his value is expected to soar.
Shakhtar manager Mircea Lucescu has said he is willing to let Willian go, but only if the fee is right for the Ukrainian side.
"I am not against letting players play for big clubs. If they pay the price, he can go," said the manager.
The attacking midfielder has two caps for Brazil and should he sign for the Blues he would join the existing Brazilian contingent of David Luiz, Ramires and Lucas Piazon at the Bridge.