The Reds, who completed a deal for Celta Vigo’s Iago Aspas on Sunday, were reported to have lodged a £23m bid for the Armenia international, who scored 25 top-flight goals last season.
Mkhitaryan has failed to report to pre-season training at the Ukrainian champions, but Palkin is adamant the Shakhtar playmaker hasn’t been in talks with Liverpool.
“Mkhitaryan has not appeared for training. We do not know if he will arrive in the near future. He will be fined,” Palkin said.
He 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.”
On Sunday, Mkhitaryan took to his Facebook page to play down speculation linking the Armenian midfielder with a switch to the 18-time English champions.
“I am happy to see that people show keen interest in my career but I would like to ask all not only to refrain from making comments but also to prevent the spread of unverified and false information,” Mkhitaryan posted on his Facebook page.
“I am not meddling with these affairs. If have a contract with a club, I just fulfil it.
“If an agreement is reached between clubs I will be informed of the details and then will accept or reject it.
“I’m not planning any media communication because I cannot comment on things of which I have no information. Professional players have rules in life and I’m obliged to respect them.
“I promise that you will hear any news first on my Facebook page or the official club website.”
ENHANCED ODDS: Get 10/1 on Arsenal to beat Chelsea