According to reports, the Süper Lig club have moved strongly into the race for the Belgian striker. AS Monaco are not involved in the discussions, while Fenerbahçe president Ali Koç is personally driving the efforts to secure the deal.
Lukaku, 33, is expected to leave Napoli in the near future. The experienced forward is in the final year of his contract with the Serie A side and is seeking a new challenge after a season that fell below expectations in Italy.
The Belgian international brings a proven goalscoring record at the highest level and would represent a significant statement signing for Fenerbahçe as they look to strengthen their attacking options for the new campaign.