Inter stopper Lucio will meet with Fenerbahce officials at some stage next week, reports Sky Sport Italia.
The 34-year-old will quit the Nerazzurri this summer and a move to Turkey is expected for the Brazilian international.
Lucio and his entourage will discuss the transfer on Wednesday, where he is expected to be offered a two-year deal with an option for a third.
The centre-back played in 42 games for the Beneamata this term, scoring two goals in the process. He joined Inter in 2009 from Bayern Munich.