The Armenian midfielder is a reported target for Liverpool, Tottenham and Borussia Dortmund and his current manager believes that moving would be a mistake
Goal reported in June that Mkhitaryan has been identified by Liverpool boss Brendan Rodgers as one of his top targets as he eyes a £42 million splurge in the summer transfer market.
The Reds face competition for the 24-year-old's signature from Borussia Dortmund, with Shakhtar CEO Sergei Palkin confirming a £19.5m bid from the Champions League finalists, while Tottenham have also been credited with an interest.
But Lucescu is at a loss to explain why Mkhitaryan, who failed to report for training last week, would want to leave the club that has helped him achieve continental recognition.
"I do not want to give comments. It's his decision, his desire. I think he is making a big mistake," Lucescu told Terrikon.
"Shakhtar are a strong club. And behind you is always 50,000 fans who will support you. We play as a team, which is fighting for the championship each year, as well as for the cup and for the Champions League - he has to appreciate that. The whole team helped him to show up in the penalty area and score.
"He is very well thought of. There is still time. I just encourage him to return to the team and get to work. Nothing happened between him and the management, between him and the other players.
"We all helped him. Perhaps even more than all the rest. When he played in the championship, I helped him to become the top scorer. If he is to join a club that surpasses [Shakhtar], I would understand his wish."
Shakhtar have already sold midfielder Fernandinho to Manchester City this transfer window after Willian moved to Anzhi Makhachkala in January.