Both clubs are battling to sign Mudryk and Shakhtar have set an asking price of £85million.
Arsenal have made a formal offer for the 22-year-old and, while their latest bid of around £60m is set to be rejected, are still front runners to sign him.
But Chelsea are considering their own bid and could turn their attempts to hijacking Arsenal’s move if they miss out on Enzo Fernandez.
Shakhtar chief Palkin is taking a leading role in the sale of Mudryk. Shakhtar sporting director Darijo Srna is also involved and is expected to be at Stamford Bridge when Chelsea play Manchester City on Thursday.
Shakhtar want a significant amount of any transfer fee for Mudryk to be paid up front and their position has been strengthened by Chelsea joining the race to sign him.
Chelsea’s move for Benfica midfielder Fernandez has stalled and it remains to be seen if they will switch to other targets.