Lucescu broke several ribs and had surgery to remove fluid from his chest cavity in the Romanian capital after the car he was driving collided with a tram on January 8.
"[I feel] a lot better," Lucescu said in comments reported by a Shakhtar spokesperson, RIA Novosti reported. "I have ahead of me a period of recuperation, but I hope to be home soon," said Lucescu, 67, who won the UEFA Cup with Shakhtar in 2009.
Former Romania national team boss Lucescu is one of Europe's most experienced managers, with spells at Inter Milan and Galatasaray. He suffered a heart attack in 2009.
Shakhtar, currently taking part in an offseason tournament in Dubai, are a point behind leaders Dinamo Kiev in the Ukrainian Premier League. The winter break ends in March.
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