The Belgium international striker has been heavily linked with a move to Everton, who he played for on loan last season.
Lukaku has never established himself at Chelsea, and his future has been cast into further doubt this close-season following the arrival of Diego Costa and the re-signing of Didier Drogba.
And the 21-year-old has heightened speculation of an imminent departure from Stamford Bridge by writing on Twitter: "Time to write a new chapter."
The post was accompanied by a picture of Lukaku, who appeared to be on a plane.
Lukaku moved to Chelsea from Anderlecht in August 2011 but he has made just 10 Premier League appearances for the London club.
He was shipped out on loan to West Brom in the 2012-13 campaign and became a fans' favourite at The Hawthorns by bagging 17 goals in 35 top-flight appearances.
A temporary switch to Goodison Park followed last term, and he found the back of the net 15 times in the Premier League.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.