The 23-year-old has impressed for Shakhtar and helped guide the club to the knockout stages of the Champions League for the first time in their history.
Willian scored twice in Shakhtar’s 6-2 aggregate win over Italian side Roma.
Arsenal boss Arsene Wenger is also reportedly keeping tabs on the midfielder.
The Daily Mail reports that Shakhtar Donetsk are looking for around £30million for the midfielder.