The Armenia international is reported to figure prominently on Brendan Rodgers' wish list, as he attempts to bring goals and creativity into Anfield.
It was suggested that an agreement was close and that Mkhitaryan was on his way to England to discuss a deal.
The 24-year-old playmaker was quick to play down those rumours, insisting he was enjoying a well-earned summer break, and Shakhtar maintain that they have received no approach.
The Ukrainian outfit have, however, revealed that Mkhitaryan is yet to report back for pre-season training - fanning the transfer flames.
Shakhtar's general manager Sergey Palkin said: "Mkhitaryan has not appeared for training. We do not know if he will arrive in the near future. He will be fined."
On the ongoing move talk, Palkin added: "He has not had any contact with Liverpool. I am confident that reports of negotiations are just rumours. Liverpool have not made an enquiry about the player.
"We have not heard that Mkhitaryan wants to leave. All questions about his behaviour need to be addressed to him."