Fenerbahce are close to agreeing terms according to a report in the Turkish newspaper Milliyet.
The article states that a Ukrainian newspaper has claimed that the experienced Romanian manager has agreed terms with Fenerbahce.
Lucescu has been closely linked with a move to Beşiktaş and Fenerbahçe in the summer.
Beşiktaş have however, rejected the notion that Lucescu would be replacing current manager Slaven Bilic.
Lucescu currently manages Shakhtar Donetsk but has been under pressure following a heady 7-0 defeat at the hands of Bayern Munich in the UEFA Champions League.
Shakhtar also find themselves seven points behind their rivals Dinamo Kiev in the Ukrainian league.
Fenerbahce are currently in their place in the Turkish Super Lig with 53 points in 25 games. The Yellow Canaries defeated both Galatasaray and Besiktas in the bast month.