The attacking midfielder has been linked with Juve this month.
Shakhtar Donetsk coach Lucescu said: "I wouldn't be surprised to see him at Juve.
"He's a guy who needs to feel loved and Dortmund have put him under too much pressure. I think his time at Borussia is over.
"I could easily see him playing behind Llorente and Tevez, or indeed any great champions. Mkhitaryan is quicker and a more willing runner than [other rumoured target Wesley] Sneijder.
"Henrikh is a complete player, he creates, wins the ball and counter attacks. Now he has to find the right environment.
"In Germany he's been greeted with suspicion because he's Armenian."
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