The Belgian striker is currently on loan with West Bromwich Albion where he has scored 10 goals this season but is targeting a successful career at Stamford Bridge once he returns from The Hawthorns.
"Yeah, that is the dream. That's what I signed for Chelsea for," Lukaku told Sky Sports News.
"My aim is to play at the Bridge and to be a legend over there in the future.
"But the time is going so really I need to keep playing. And hopefully in the next few years become one of the key elements at the Bridge."