However, club president Florentino Pérez has appeared to silence those claims by insisting that Real Madrid will focus on developing their next generation, as opposed to spending big in the transfer market on a new squad of Galácticos.
A report from Spanish outlet AS is also signing from the same hymn sheet as Real Madrid's president, claiming that a move for Hazard has likely been ruled out because of Bale's superior commercial value.
It is suggested that although Hazard is among the top 10 highest earning players in the world through commercial deals, his off-pitch value is still significantly less than that of Real Madrid's star Welshman.
As a result, Los Blancos will put all their eggs in one basket this summer and hope that Bale can fill the shoes of Ronaldo, who will now rule the roost in Turin.
The 29-year-old has been part of the set up in Madrid since 2013 after he completed a world record move - at the time at least - to the Santiago Bernabéu. Bale has gone on to make 198 appearances to the club, scoring 88 goals and claiming 57 assists.