The La Liga giants are said to be in indirect contact with the Blues duo.
And according to the Daily Mail, the Belgian pair would be willing to make the move despite their happiness at Chelsea
Hazard has apparently been picked out by Madrid as a key summer target with Zinedine Zidane determined to land the attacker.
Convincing Chelsea owner Roman Abramovich to part with Hazard will be difficult, as a huge fee is required.
Eden Hazard and Thibaut Courtois could both leave Chelsea this summer for Real Madrid
Top five Chelsea players this season
Wed, March 22, 2017
Who are the top five Chelsea players in the Premier League this season, according to WhoScored.com?
1 of 6
Which Chelsea stars have performed best in the Premier League this season?
Antonio Conte is a big fan of the former Juventus hitman
However, The Guardian add Madrid hope the desire of the 26-year-old to join and making players available to Chelsea in return will make an agreement easier to reach.
Get Quotes on Home Insurance
Madrid president Florentino Perez is reportedly ready to offer both striker Alvaro Morata and unsettled playmaker James Rodriguez as part of the deal.
Antonio Conte is a big fan of the former Juventus hitman, having eyed a move for the 24-year-old last summer.
And it is claimed Chelsea goalkeeper Courtois and Madrid forward Morata switching teams will be the more straightforward half of the business.
Ex-Atletico Madrid shot-stopper Courtois is open to a return to Spain’s capital, despite public claims he is content at Stamford Bridge.
And Chelsea are apparently confident they can find a new keeper too, with Madrid focusing attention on the Belgian rather than David De Gea at Manchester United due to the difficulty in capturing him.
Meanwhile, Morata is also open to playing in the Premier League.
Madrid intend to bid for Hazard ahead of the summer transfer window, with at least a part-exchange of the four players possible.