Website Football.London is reporting that the Blues are looking at the Brazil worldwide as a favorable candidate to fill Courtois' boots should the Belgian force through a move.
Hazard has been linked with a move to Madrid since the end of last season and the report also claims that Tottenham striker Harry Kane is wanted by the Galacticos.
Cristiano Ronaldo and Zinedine Zidane, both paramount to Madrid's three Champions League titles in a row, have sensationally quit the club.
Real Madrid have been linked with Hazard but, according to Transfermarketweb, the Belgium global has reportedly agreed to sign for the Catalan giants and will move in a £80m deal. "Eden Hazard will be leaving for a big, big club".
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Recently, Hazard admitted that Madrid would be any footballer's dream, regardless of the fact that Zidane is no longer the manager.
"My future doesn't depend on Conte but this is an important development".
His family still reside in Madrid from his time on-loan at Atletico.
Chelsea are desperate for Hazard to sign a new long-term deal and are on the verge of appointing a head coach more to the liking of the Belgian.