The Blancos saw a talismanic presence head for the exits over the summer, with a €100 million (£88m/$116m) deal taking a five-time Ballon d’Or winner to Juventus.
With Ronaldo now strutting his stuff in Serie A, those left behind in Madrid have struggled to find their attacking spark in 2018-19 – going four games without a goal prior to the international break.
Transfer talk is building as a result, with the Liga giants expected to move for top targets either in January or early next summer.
Belgium international Hazard is considered to figure prominently on their wish list and, with the 27-year-old continuing to hint at a switch, Rivaldo believes it is only a matter of time before that deal is done.
The former Barcelona star, who was named World Player of the Year in 1999, told Betfair: “The Belgian attacker is a great player and could be a very good option for his 'dream club' Real Madrid in the next transfer window. Hazard was excellent for Belgium at the World Cup and has started the new Premier League season very well.
“For that reason, Real Madrid should be considering his signing, especially given their recent poor form and Hazard's stated desire to play at the Bernabeu.
“This kind of move could be good for the club and fans, as the arrival of a top player would give a much needed boost after Cristiano Ronaldo's departure. Hazard is very talented, scores goals and assists a lot - he's a spectacular player who I particularly appreciate.
“In my opinion, Hazard could play even better at Real Madrid than in England as Spanish football gives a little more freedom to the players. So if he is already producing masterpieces in the Premier League, he could get even better in Spain.”
Hazard has netted seven times in the Premier League this season to lead the likes of Sergio Aguero and Harry Kane in the race for the Golden Boot.
He has admitted that the opportunity to move to Madrid at some stage in his career would be a dream, with there no suggestion that he will be looking to extend a contract at Stamford Bridge due to expire in 2020.