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.
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.
