Shakhtar Donetsk manager Lucescu is close to agreeing terms with Fenerbahçe to take over as head coach in the summer according to Turkish newspaper Sabah.
Lucescu has been closely linked with the Yellow Canaries over recent weeks and is reported to be considering his options due to the security situation in Ukraine.
The Romanian manager currently manages Shakhtar Donetsk but has been under pressure following a humiliating 7-0 defeat at the hands of Bayern Munich in the UEFA Champions League.
The experienced manager has a lot of experience coaching in Turkey.
Lucescu previously managed Beşiktaş and won the Süper Lig as Black Eagles head coach in 2002-03.
The former Beşiktaş boss also coached Galatasaray between the 2000-02 seasons, during which time he won the UEFA Super Cup against Real Madrid and reached the quarter-finals in the 2000–01 UEFA Champions League.
Lucescu guided Galatasaray to the Super Lig title the following season however, was sacked despite winning the title.
Shakhtar also find themselves seven points behind their rivals Dinamo Kiev in the Ukrainian league.