Ihor Surkis says he has no intention of selling to the Toffees.
Toffees boss Roberto Martinez, meanwhile, has also been credited with renewing his interest, according to The Express, but Yarmolenko's long-term future remains up in there somewhat.
The Ukrainian star, who was linked with a move away last summer before signing a contract extension until 2020, might well end up in the Premier League, but Surkis says that it will almost certainly not be at Goodison Park.
"If we get an offer that satisfies Dynamo and Yarmolenko wants to go to the club, I will let him. My position is that we should not let Yarmolenko go to such clubs as Everton and Stoke City," he told Futbol 1, via Soccerway.
"I, as president of the club, had a winter offer from China completely arranged, but Yarmolenko did not even come to the meeting with the sports director of the Chinese squad. Andriy said that he wants to play in the Bundesliga and the English Premier League.
"At 26 it is time to move to a top club. He is a top footballer so should try and go to a top club."
Everton fans have seen first hand how good the player is, having dismantled them for Dynamo in a Europa League quarter-final tie last season.
It is perhaps a touch surprising that he has lasted so long in a perceived inferior division comparatively speaking and, at 26, the clock is running out for him to make his mark on one of Europe's elite leagues. Time will tell whether that could be the Premier League.