The striker, who only turned 17 in May, was the top scorer in Belgian League last season for Anderlecht and has been linked with a host of top clubs.
Dubbed the 'new Drogba' because of his looks and physique, Lukaku is currently with the Belgium squad in Finland where he hopes to earn his second international cap.
Jose Mourinho is believed to be a big admirer of the 6'3" phenomenon but Lukaku has said he intends to stay with Anderlecht.
"I'm staying. My desire is to play in the Champions League with this club and continue my studies in Brussels," he told Spanish newspaper Marca.