The Yellow Canaries have made an enquiry for Lukaku and are in talks with his club in an attempt to bring him to Turkey over the summer.
The full-back would replace Caner Erkin who joined Inter as a free-agent last month before Euro 2016.
Lukaku is however, a self professed Arsenal fan although he also revealed that he could get behind just about any n0n-relegatin battling Premier League side.
“Do I see myself as Premier League-bound?” Lukaku told The Set Pieces.
“I don’t know, but it’s a league that would suit me. I have always been a fan of Arsenal, but I am mad about every Premier League club as long as the club doesn’t have to fight against relegation.”
Fenerbahce finished last season as runners-up and lost the Turkish Cup final but still qualified for the Champions League next season.
Lukaku would be a first choice player at the Yellow Canaries if he were to make the move but he is not expected to make a decision until after Euro 2016.