The Belgium international struggled for playing time in his first season in the Premier League after his transfer from Anderlecht in August 2011, but scored 17 league goals while on loan at West Brom last term.
As a result, Lukaku now looks set to compete with Fernando Torres and Demba Ba for a starting berth at Chelsea, and the 20-year-old has acknowledged he must step up personally and for the club.
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"I know people are saying nice things about me but I am trying not to think too much about the future. I’m living day by day. I just want to score as many goals as possible."
Lukaku went on to praise the depth of the squad that won the Europa League and reached the semi-finals of the FA Cup and Capital One Cup last season, but refused to reveal whether he had discussed his role in the side with Jose Mourinho.
"With Juan Mata, Oscar, Eden Hazard and the others we have some great young players," he added.
"For a club the size of Chelsea you need a strong squad like that. There are plenty of striking options but it is up to us to perform.
"I am happy to be coached by Mourinho. Have I been given any idea on where I am in the pecking order? That’s confidential."