The Reds and Spurs are both reported to be chasing the highly-rated Armenian playmaker as they look to bolster their attacking options this summer.
Liverpool are rumoured to be leading the chase for Mkhitaryan, but Lucescu insists there is still time for the 24-year-old to change his mind and stay at Shakhtar.
"It is his decision, his desire, but there is still time for him to change his mind, because I think he is making a big mistake," Lucescu is quoted as saying in the Daily Mirror.
"I can understand the urge to leave if he has a chance to go to a club that surpasses Shakhtar, like Barcelona or Real Madrid, but not many clubs are beyond our level - not clubs like Liverpool or Tottenham.
"We are a strong club with 50,000 passionate supporters every week, and every year we are fighting for the league, the cups and the Champions League.
"This place is good for him, and he is making a mistake if he thinks there are many teams above this level."