He has just one year remaining on his contract at Chelsea.
A deal for top target Jordan Pickford - another who impressed at the World Cup - is proving hard to complete, with Butland viewed as an adequate alternative.
Now Madrid want to include Willian in their swoop for Courtois with the Brazilian making up around £65m of the combined fee.
However, the same story says that Chelsea FC are "determined" not to sell Hazard this summer and they feel that handing him the captain's armband at Stamford Bridge may help to convince him to stay at the club.
Chelsea have until the August 9 transfer deadline to make a move for a new keeper with Stoke's Jack Butland easier to sign than first-choice target Jordan Pickford who Everton do not want to release.
Chelsea transfer news Maarten Stekelenburg signed a new two-year deal with Everton on Monday
If reports in Spain are to be believed then Real Madrid are not desperate to replace Cristiano Ronaldo with a big name signing rather the club has put its faith in existing crop of players, especially Gareth Bale.
He was regularly shackled to the right-side of a midfield quartet under Zinedine Zidane.
According to the Mail, Madrid are "seriously considering" a double bid of £100m for Willian and Thibaut Courtois. However, the La Liga champions opted to recruit the player's compatriot, Malcom as an attacking signing.
As well all know by now, Manchester United have been chasing Willian this summer, as José Mourinho searches for a natural wide player to shuttle up and down the wing for 90 minutes, offering very little other than a high work rate.
Chelsea are ready to offer the veteran goalkeeper a one-year deal to move to Stamford Bridge with Green expected to finalise his move later this week.
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