According to Phil Cadden in the Sun, Los Blancos are already in talks with Lukaku's agent, Mino Raiola, while the player himself reportedly believes he can only advance his career "by appearing regularly in the Champions League."
Despite being only 22, the imposing Belgian striker is already one of the most dangerous forwards in the English top flight, having reached double figures for goals in each of the last four seasons, per WhoScored.com.
His recent solo effort in the FA Cup against former club Chelsea was the perfect illustration of the blend of physicality and poise Lukaku offers in attack, while he is rightfully high on confidence as well, per BT Sport Football:
BT Sport Football @btsportfootball
.@RomeluLukaku9 talks through his incredible solo goal for @Everton against his former club @ChelseaFC. https://t.co/7bZACrw8nz3/19/2016, 12:31:52 PM
Cadden reported "friends of Lukaku insist [he] loves playing for the Toffees," but the fact Roberto Martinez's side lie 12th in the Premier League is not going to encourage him to stay for long.
The potential opportunity to play at Real will undoubtedly be hugely tempting to Lukaku.
While he only moved to Goodison Park permanently less than two years ago—for £28 million—his prospects have worsened despite his improvement.
He has the ability to be one of the top strikers in the world, and Everton would find it difficult to turn down a bid for Lukaku that would see them more than double their money.
One of Lukaku's reservations about making a move to Real could be the fear he may not get much regular first-team football given the strength of the Madrid squad.
However, Cadden reports Real president Florentino Perez is planning to move on Karim Benzema in the summer, and the Frenchman is Los Blancos' only out-and-out striker.
If that is the case, then Lukaku could slot into the Madrid side in the main forward's role and join an attacking line that includes Gareth Bale and Cristiano Ronaldo.
Moving on Benzema, 28, would be a big risk on Perez's part, as, though he flies under the radar in comparison to Bale and Ronaldo, the France international is arguably the key component in the attacking unit, per football writer Graham Ruthven:
Graham Ruthven @grahamruthven
That Real Madrid game was fantastic. Karim Benzema makes such a difference to that team. They need him.3/20/2016, 10:19:42 PM
Lukaku, though, is one of the best attacking prospects in the world, and the fact he is still young and still improving makes him a very attractive target for the Bernabeu outfit.