Mudryk, who has finally come good for the Blues after a miserable first six months at the club, wants to be joined by another Shakhtar Donetsk star.
He is calling on the Blues to bring in old teammate Georgiy Sudakov in January.
Gazzetta dello Sport state that Mudryk has been telling co-owner Todd Boehly about the talent.
He wants to see the 21-year-old playing with him at Stamford Bridge in the near future.
However, boss Mauricio Pochettino is more eager to bring in a central defender.