The Belgium international striker is currently on loan at West Brom and has scored nine Premier League goals for the Baggies this season.
But the 19-year-old sees his long-term future at Stamford Bridge and believes there is still time for him to become a star with the Blues.
"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.
The signing of Demba Ba in January looks to have made Lukaku's task of earning a starting spot at Chelsea a trickier one but the powerful forward is undaunted by the competition.
"That's the thing when you play for Chelsea. They will always sign big players," he added.
"So now it is up to me to show I can go over there and play and do the same as he does now."