Arsenal are among the clubs to have been heavily linked with Morata in recent times and Real boss Carlo Ancelotti appeared to admit earlier this week that the 21-year-old was set to leave the Santiago Bernabeu in search of more regular first-team football.
According to The Daily Star, Real are targeting £25 million-rated Lukaku as the man to fill the void that would be left by Morata's departure, with cross-city rivals Atletico believed to be interested in his signature along with a whole host of other European clubs including Roma and Wolfsburg.
The situation regarding Lukaku's future is certainly a puzzling one that is sure to both intrigue and confuse the majority of Chelsea fans.
With the powerful Belgian - who will have to contend with the pressure of leading his country's attack at the World Cup this summer following an injury to compatriot Christian Benteke - first having thrived back in 2012/13 during a season-long loan spell at West Brom, many expected Jose Mourinho to bring Lukaku back to Stamford Bridge for the start of his second reign in charge of the club in order for him to stake his claim for a regular starting berth alongside the trio of Fernando Torres, Demba Ba and Samuel Eto'o.
Despite the player having made two substitute appearances at the very start of the last campaign, however, Chelsea fans appeared extremely frustrated with the decision to once again allow Lukaku to depart the club on a temporary basis.
Consistent with his obvious talent and enormous potential, Lukaku once again proved his ability and desire to compete with the very best in the Premier League, this time positively thriving at Everton under the tutelage of the affable Roberto Martinez.
And while you might be forgiven for thinking that - given the departure of Eto'o and the persistent question marks surrounding the respective futures of Torres and Ba - it now must surely be time to give the 21-year-old an extended opportunity to repeat that stellar form in West London, such a possibility appears questionable at best given the wealth of rumours of late that have hinted at a move elsewhere.
Whether Real Madrid would be an ideal next destination for Lukaku, however, is certainly up for debate.
Despite not previously enjoying a favourable status among the club's fervent fanbase, French international Karim Benzema has established himself as the undisputed first-choice striker in the Spanish capital after linking-up very well indeed with the formidable duo of Cristiano Ronaldo and Gareth Bale.
If he were to make the move to Real, therefore, it is highly unlikely that Lukaku will be afforded the regular chances to start that he is evidently seeking.
At this crucial stage of his development and his career, as those aforementioned loan stints have demonstrated, it is of vital importance that he does not simply settle for a place on the substitute's bench, irrespective of the potential financial merits that a move to a place like Madrid may promise.
On the other side of this particular story, it is not too tricky to see the merits of a potential switch to Arsenal for Morata.
Following the departure of the much-maligned Nicklas Bendtner, Arsene Wenger is in dire need of a better striker to reduce his reliance on Olivier Giroud.
While Morata is perhaps not as experienced a player as some Gunners enthusiasts would like to see, he has showcased sporadic examples of real goalscoring nous during his formative years at Real and also during remarkably prolific spells in the Spanish youth setup.