Stoke, who have already added six players to their squad so far this summer, are looking to complete their transfer business with a marquee signing to play on the wing.
After missing out on Yevhen Konoplyanka and giving up on Xherdan Shaqiri, the Potters have turned their attention to Yarmolenko.
Dynamo Kiev manager Sergei Rebrov said last week he felt the 25-year-old should hold out for a move to a Champions League club, but Yarmolenko has refused to rule out a move to a club he played against in the Europa League in 2011.
Stoke were renowned for their direct and physical approach under Tony Pulis at the time, but Yarmolenko acknowledges Hughes, who has signed the likes of Marko Arnautovic and Bojan in his two years at the club, has transformed the team’s way of playing.
“Back then (in 2011), Stoke were completely different,” Yarmolenko told Ukrainian newspaper Sport Express. “They no longer hit balls at random and take long throw-ins.”
Stoke are reported to have made a 20million euros offer for Yarmolenko, and the Ukraine international fears he could regret passing up the chance to move to the Premier League.
He said: “Will I stay or go? “I have proposals which I am deliberating on at the moment. All should become clearer in the next month.
“My attitude has not changed. I have been with Dynamo since I was a child and they have raised me and made me the person I am today.
“I want my home club to get decent compensation (if I leave).
“I still have another year on my contract and the negotiations with any potential buyers should go directly through Dynamo president Ihor Surkis.
“You may not believe me, but the financial side of any future deal is not critical.
“Money, of course, important, but much more important, no matter how corny it sounds, is the prospect of development and growth.
“Really it’s about crying at the age of 30 if you have not had the chance to test yourself once in a serious championship.”