But the Ukrainian club will insist on a fee in the region of £20m for a player who is reportedly keen to move to the Premier League this month.
The Brazil international recently failed to return to Donetsk in time for the club's winter training sessions, leading Shakhtar coach Mircea Lucescu to brand him as 'unprofessional.'
And the report claims Shakhtar, who qualified for the Champions League last-16 at the expense of Chelsea, are willing to sell Willian for the right price.
The Ukraine champions signed Brazilian playmaker Taison for £12.4m from Metalist Kharkhiv earlier this month, leading to speculation he was recruited as a replacement for wantaway Willian.
The Standard claim that Shakhtar's resolve to hold on to Willian this month has weakened, and the club could be persuaded to sell the Brazil playmaker - if a bid around £20m is forthcoming.
Chelsea and Tottenham are both reportedly interested in the midfielder, who can play in a number of advanced positions, and Willian himself is believed to be willing to talk to either club - although the Stamford Bridge side are thought to be better positioned to make a higher offer.