The Spanish side are expected to overhaul their squad at the end of the season having missed out on the Champions League and La Liga football titles, and the English Premier League duo are high on their wish-list.
In addition, Belgian journalist Kristof Terreur told Sky Sports that Hazard sees Zidane as an inspiration, and that the Frenchman's return as Real manager meant Hazard's move to the Bernabeu was "falling into place".
The only goal came when Adri Embarba sent Real goalkeeper Thibaut Courtois the wrong way with a penalty midway through the first haalf, giving Rayo a deserved lead after an ambitious start in front of a typically raucous home crowd.
Madrid's display: "We have to apologise for the account we gave of ourselves. We should be angry about everything we did today". However, I think that all of them are looking to play. I'm responsible for it. "But we have to apologise for our performance today, all of us".
VAR played a crucial role in Rayo's first victory over Madrid since 1997 - referee Pablo Gonzalez Fuertes changing his initial decision not to award the hosts a penalty for a foul by Jesus Vallejo.
Where is it all going wrong for Manchester United?
Spurs are now third on 70 points with Chelsea (67), Arsenal (66) and United (64) behind. We just have to make sure we give ourselves a chance on Sunday.
Real were also without their top scorer as Karim Benzema, who had netted 10 times in his last eight games, was missing with a hamstring injury, while captain Sergio Ramos was also out.
Embarba nearly caught Courtois out with a cross-shot shortly after the restart, before Madrid's goalkeeper made a smart stop to deny Bebe.
Zidane said last week that the league would be the club's first priority from August but, even with new signings and fresh motivation, it could prove hard to flick the switch.
Madrid wanted their own spot-kick when Mariano Diaz took a tumble from a corner but Gonzalez was unmoved, and the second half was surprisingly comfortable for Rayo.
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