The Belgian international has earned a number of plaudits for his performances during a loan stint with West Bromwich Albion so far this campaign, which in turn has resulted in speculation that he could join the Baggies on a permanent basis.
However, the 19-year-old has revealed that he would like his future to be with the Londoners.
"That's the dream. That is what I signed for Chelsea for. My aim is to play at Stamford Bridge and to be a legend there in the future. I need to keep playing and over the next couple of years be a key element at the Bridge," he told Sky Sports News.
The Blues recently recruited Demba Ba, who operates in a similar striking role as Lukaku. Rather than feel threatened by the presence of other centre-forwards, Lukaku has instead insisted that it will be up to him to prove his worth.
"When you play for Chelsea they will always sign big players so now it is up to me to show that I can do the same as [Ba] does now," he added.
Lukaku has scored nine goals for West Brom.