Yarmolenko's agent Vadim Shabily has been spotted at Goodison Park on more than one occasion and even posted a picture of himself alongside Roberto Martinez.
The 55-cap Ukraine international signed a five-year deal last year but Dymamo chief Sergei Rebrov fears his future hinges on president Ihor Surki.
Speaking earlier this month, Rebrov said: "I can see his progress and that other teams are interested in him but it all depends on his relationship with the president.