Chelsea are keen but refusing to pay Everton's huge asking price.
The striker has been linked with an exit from Everton for several months, with him and his agent making it clear he wants to play for a Champions League club.
So far former club Chelsea are the only ones to register a firm interest, with the London Evening Standard reporting that they were locked in negotiations to try to bring him back to Stamford Bridge.
However, a deal is far from being agreed as Everton refused to lower their mammoth £75 million asking price for the Belgium international.
And according to the London Evening Standard, Lukaku is now considering handing in an official transfer request to try to secure an exit.
They report that his reluctance to upset the Everton fan base, who have supported him strongly since he joined, is stopping him doing so at this moment in time.
However with Chelsea only willing to pay up to £67 million to sign him, that stance may change before the end of the transfer window.