The striker has again insisted he is not keen on another loan spell and instead wants to prove himself at Stamford Bridge this season.
The striker was a revelation during his season-long loan at West Brom last term, scoring 17 Premier League goals in 35 appearances, including a hat-trick against champions Manchester United on the final day.
Only five players found the net more times than the 20-year-old in the Premier League, none of which play for Chelsea, fueling reported interest from several clubs but Lukaku is focusing solely on forcing his way into Jose Mourinho’s plans.
"It feels good," said Lukaku of the interest in him during an interview with The Sunday Mirror.
"I knew that, if I performed well, people would make a lot of requests for me. But I’m a Chelsea player and happy to be here. It’s up to me. If I do well, I will play. I have always felt like a Chelsea player, even at West Brom."
Belgium international Lukaku has so far made just eight Premier League appearances for Chelsea following his 2011 move from Anderlecht.
Being an emerging young player at Stamford Bridge is difficult, as Lukaku is quick to point out and knows only too well, due to the strength in depth and the club’s financial clout.
Lukaku, though, relishes the competition from the likes of Fernando Torres and Demba Ba for a place in Mourinho’s side on a weekly basis.
"It’s not easy at Chelsea, it’s not easy at all," he said. "You have to show yourself every day because you know how big the competition is and, if you don’t do well, there is always a player that can take your place.
"Of course, I think I can get into the first team at Chelsea. But there is still room for improvement."