Reports in Spain had suggested an agreement had been struck between Hazard and Chelsea's transfer chief Marina Granovskaia to listen to any approaches from Real Madrid, but no talks have yet started.
Antonio Conte has led Chelsea back to the top of the Premier League and they are 10 points clear of the chasing pack, while Hazard is said to be loving life again at Stamford Bridge after a difficult season last year.
Real Madrid boss Zidane has always liked Hazard, who idolised the former France international growing up, but Chelsea will play hard ball with Madrid over any approach.
Hazard is also unlikely to push for a move away as he is settled in London with his young family and he is happy with the football that Chelsea are playing under Conte.
Real Madrid are prioritising new signings in other positions too and they have made Hazard's Blues team-mate Thibaut Courtois their number one transfer target as they look to sign a 'galactico' goalkeeper.
Chelsea will look to Atletico Madrid's Jan Oblak as a replacement, if they lose Courtois, but they have made no such contingency plan with Hazard for the summer.
Meanwhile, a source close to Conte has told Goal that the Chelsea manager talks about Alvaro Morata "almost every day" and it appears that the Madrid striker will be one of his biggest targets ahead of the summer transfer window.
However, a swap deal involving Chelsea and Real Madrid players is unlikely due to the complexity involved in combining deals, with any interest in James Rodriguez appearing to be minimal.