Real have been linked with Hazard, who is still yet to agree a new contract with Chelsea, for well over a year on and off. Speculation has significantly grown in recent weeks.
But, according to Marca, the reigning European champions are prepared to cool any interest in Hazard to give 21-year-old Asensio a renewed chance to shine.
"Why would we bring in the Belgian if we have Asensio?" is the quote attributed to an unnamed senior board member at the Bernabeu.
Carefully managed so far this season, huge things are expected of the former Real Mallorca youngster and Marca suggest that the 3-0 Clásico loss at the hands of Barcelona shortly before Christmas will serve as a 'turning point' for changes in the capital.
Asensio is therefore in line to become more regular as Zinedine Zidane looks to shake things up and get Real back on track after a mixed first half of the season.
Prioritising the development of Asensio over the Galacticos style capture of Hazard would certainly be in keeping with the club's evolving transfer policy in recent years - no 'Galactico' has been bought since James Rodriguez joined from Monaco in the summer of 2014.
Curiously, the story from Marca states exactly the opposite on the future of Hazard as an 'exclusive' claim from The Sun. The British tabloid suggests that Real are preparing a £120m offer for the Belgian, one that would make him one of the most expensive players of all time.
Given the conflicting nature of the stories that emerged around the same time, only one be correct.