The 18-year-old striker, who made his debut at the tender age of 16 for the Belgian giants, has also caught the eye of Premier League rivals Arsenal, Manchester City and Tottenham Hotspur.
Although Anderlecht have previously underlined their intention to keep hold of their highly-coveted player, it appears that the Belgian international is set to move on with Anderlecht General Manager Herman van Holsbeeck admitting that the two parties are holding talks.
"There is still a long way to go in the negotiations [for Lukaku],” he told Sky Sports.
"We are indeed negotiating with Chelsea, but there are other clubs we are talking to.
"It [a deal] could happen in the next half hour, it could take until August 31, that is football."
Meanwhile, Chelsea look set to snare another Belgian youngster with the transfer of Genk midfielder Kevin de Bruyne, who has confessed his desire to join the West London outfit.
"I have had time to think about my future and I would love to join Chelsea, but the important thing next season is that I play," he said.
"And with Chelsea there is not that guarantee, but there would be at Anderlecht and they would be ideal springboard for me.
"I know Genk are in the Champions League but they must get through two rounds anyway, and if I can improve sporting wise and obviously financially, then I hope Genk will not put any obstacles in my way.
Although reports have suggested that Chelsea would sign De Bruyne and then loan him to Anderlecht in order to pave the way for a move for Lukaku, De Bruyne’s agent has denied these claims, stating that he would willingly join Anderlecht.
"No, that is not the case with this," Patrick de Koster said. "Kevin, though, is happy with the prospect of joining Anderlecht - he has stated that himself.
"He knows Chelsea have a history of this [loaning out players] and if you do well you will get your chance.
"And, yes, although he would benefit financially from this move, he is young and this is about his career and sporting opportunity."
