The 31-year-old looks ready to quit Stamford Bridge once his contract expires this summer.
Real were offered to sign the Brazilian, who is also wanted by Arsenal and Tottenham.
ButThe Mirror says the Spanish giants don't want to meet his demand of a three-year contract.
Although he is an admirer of Willian, manager Zinedine Zidane has told the club to move onto other targets.
The man himself has professed his desire to stay in England in the past, with his family settled in London.
Speaking to Sky Sports, his agent Kia Joorabachian admits Chelsea don't want to meet his demands.
"Willian wanted to sign a three-year contract to achieve things he wanted to achieve over the next three years, and see where his career take him from there.
"Chelsea's policy [for players over 30] only allows two [years], so that's where the stumbling block was.