Hazard left Stamford Bridge to head to the Spanish capital with the Blues reportedly paid just £36m up front.
Having been banned from making any transfers last summer, Chelsea boss Frank Lampard has been busy so far during this transfer window.
Kai Havertz, Timo Werner and Hakim Ziyech have headed to Stamford Bridge, along with Ben Chilwell, Thiago Silva and Malang Sarr.
And the Blues funds have reportedly been boosted by their deal with Real Madrid over the Hazard fee.
Voetball claim that Real will give the Premier League giants £50m this summer with an additional £57m being transferred next year.
It takes the total fee that Los Blancos will spend on Hazard, who struggled in his first season at the Bernabeu, up to £143m.
The Belgian struggled with injuries during his debut Madrid campaign, making just 22 appearances in all competitions and scoring just once.
And Real team-mate Luka Modric has told Hazard he has to be 100 per cent next season.
"Eden is a great guy and a special player, but he was playing with pain and when you're on the pitch, people always expect the best. They don't care if you have little problems," Modric told AFP.
"I spoke to him and said, 'Eden maybe you need not to play now and recover because next season we need you at your best.
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“‘This is a season where you're getting to know everything but next season you need to be 100 per cent because if not, it's going to be difficult'.
"Hopefully he comes back without any problems and then I'm sure he'll show his potential and why the club bought him because we will need him a lot."