The Gunners are keen to sign the Ukraine international this winter.
Shakhtar Donetsk CEO Sergei Palkin says the club are yet to receive a suitable offer for Mykhaylo Mudryk.
Arsenal are leading the race to sign the winger, despite interest from a host of other European clubs.
Shakhtar reportedly want €100m for Mudryk. But English sources have claimed they might allow his exit for a lower fee this January.
Asked by the Athletic about a possible winter move for Mudryk, Palkin confirmed his side are in negotiations to sell the forward.
“To be honest, I do not know,” he said. “At the moment, we are quite far from what we want and what clubs propose. It’s not so far, but it is not what we need.
“We have discussions. One club, another club, they negotiate. We are in the process. Will it close this month? I don’t know.
“It is maybe 50/50 with regards to the winter transfer window. I don’t want to talk about figures now. We are in discussions. We have interest from some English clubs and we are in the process.”
Palkin went on to suggest that Arsenal are not the only English side
“Every day, I read about another English club,” he added.
“If you believe the newspapers, it is all of them. But to be honest, it is true as I have had contact from many clubs. A lot of them are involved in this process.”