The Belgian is likely to be on the move this summer, despite his excellent form while out on loan over the past two seasons with West Brom and Everton. He managed 32 goals in 66 games with both of those clubs, but could well be on his way out of Stamford Bridge.
Sold in the summer?
Chelsea are believed to have put a £25 million price tag on the 21-year-old, with Everton interested in signing him permanently and Atletico Madrid said to be keen on him too.
Tottenham also threw their hat into the ring as they look to bolster their forward line, with Lukaku's agent confirming in April that an approach had been made.
However that appears to be something of a non-starter, with the Daily Mail claiming that Chelsea have no intention of selling the striker to Tottenham.
The two London-based clubs share something of a fractious relationship when it comes to transfers. Spurs defied Luka Modric's wishes by refusing to do business with Chelsea when they declared an interest in the Croatian ace back in 2011.
Chelsea got their own back by beating Tottenham to Oscar in 2012, while the north London club were reportedly irate at the Blues late, late swoop for Brazilian Willian last year when he was undergoing a medical with Spurs.
Previously Chelsea boss Jose Mourinho has been reluctant to sell to teams he sees as a threat, which is what he did by blocking Demba Ba's switch to Arsenal in 2013, however how much of a danger he views Tottenham in the Premier League remains to be seen.
Interestingly the Daily Mail add that with Tottenham out of the picture, Liverpool could well swoop.
Brendan Rodgers has been in a hurry to get his transfer business at Liverpool done quickly so far, and could well sense an opportunity with Lukaku.
Once again, whether Chelsea will do business with Liverpool remains to be seen, but they sold Juan Mata to Manchester United when the price was right, and may do so again in order to let him head to Anfield.
Given that Liverpool can now offer Champions League football, a switch to Merseyside may appeal for Lukaku, although it is unclear where he would fit in a team that already contains Luis Suarez and Daniel Sturridge.
Atletico Madrid can't be discounted in the race as they search for a replacement for Diego Costa, who should have his switch to Stamford Bridge confirmed soon.