The Spanish giants have emerged as surprise contenders for Lukaku's signature, while Everton are hopeful of securing the Belgian's services on a permanent basis having taken him on loan last season.
According to the Telegraph, Chelsea have warned his suitors that they will have to stump up £30 million for Lukaku this summer; that figure could well be out of Everton's reach which would then leave Real Madrid clear to swoop if they so wished.
The likes of Juventus, Wolfsburg and even Tottenham have been linked with the 21-year-old in recent weeks, but it seems as though Everton are in the driving seat. The Telegraph say that the Toffees only want to pay around £23 million for the former Anderlecht man. If they are unable to negotiate a fee with Chelsea then another loan deal may be a viable alternative.
Despite that Chelsea are keen on either selling Lukaku or keeping him; his current contract runs until 2016 which means that if he goes out on loan he would return to Stamford Bridge with only a year left on his deal and his market value significantly lessened.
The arrival of both Diego Costa and Didier Drogba at Chelsea this summer means that Lukaku's chances of regular first team action are slim, while it would seem as though the striker shares an uneasy relationship with boss Jose Mourinho.
The Special One was seemingly unhappy with Lukaku for forcing his way out of Chelsea on loan last term, while the Blues struggled for goals. The Belgian hit out at Mourinho by claiming that they hadn't spoken during his time on Merseyside - prompting the Chelsea boss to hit back.
‘Romelu is a young boy who likes to speak,’ he said in November. ‘The only thing he didn’t say is why he went to Everton on loan. That’s the only thing he never says. My last contact with him was to tell him exactly that. Why do you never say why you are not here?
'It’s something he should say, the reason why he’s not with Chelsea and is in Everton. There are things in our lives that we have to keep private but one day he scored and said he hoped Jose was watching.
'It was like saying: “Why did he let me go?” And that’s what I’m telling him now: “Tell the country why you left.” When you enjoy to speak, speak everything.
'Don’t speak only half of it. Speak everything. It’s a simple question: Why did you leave Chelsea? Ask him.’
Having spent the last two seasons out on loan with West Brom and Everton, Lukaku has proven himself as a Premier League goalscorer, finding the back of the net 32 times in 66 games.