The Toffees striker scored 18 times in 37 Premier League games in an otherwise disappointing season for the Merseyside outfit.
Lukaku moved to Goodison Park in a £28.5m deal from Chelsea in 2014 after Jose Mourinho deemed the Belgium international surplus to requirements.
However, the 23-year-old has been linked with a £60m return to Stamford Bridge ahead of the appointment of Antonio Conte as their next manager.
And the Everton star confirmed his desire to quit the Toffees in the summer transfer window ahead of Belgium’s Euro 2016 campaign in France.
“I’m at a point where I have to make a good career choice,” Lukaku is reported as saying by the Daily Star.
“We have a new investor at Everton [Farhad Moshiri], and out of courtesy I will listen to what he has to say.
“But I have my own ideas in mind. I want to win titles. I have had a very good season, but it is time for me to write myself a CV. That is why I play football.
“I get that trophy-winning mindset from Chelsea.”
Chelsea finished in ninth place in the Premier League table last season after a woeful defence of their top-flight crown.
Lukaku has netted 43 times in 108 appearances for Everton during a three-year spell at Goodison Park.
The Belgian forward made just 15 appearances for Chelsea during his spell at Stamford Bridge.
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