Courtois' Chelsea FC contract is due to expire next summer and the Blues are likely to want to avoid the possibility of losing him on a free transfer next year.
Willian's return match came after Brazil made it to the quarter-final of the World Cup, but they were knocked out by Eden Hazard and Thibaut Courtois's Belgium, after a 2-1 defeat.
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"The only cub who made an offer for me was Barcelona", revealed the player.
Willian added: "I have my head here and I intend to continue in the club unless the club wants to sell me".
Their search has so far hit a brick wall, leaving the West London club to switch their attention to Stoke City and England 'keeper Jack Butland, according to reports by Sky Sports.
While Courtois is attempting to engineer a move away, Hazard has decided not to agitate for his own switch to Real. "I have been reading everywhere that Chelsea are saying it is up to Thibaut", Henrotay had told the Sun.
"I want them to stay, because we have top players with the confidence", Luiz said. Chelsea, on the other hand, have reportedly been reluctant to part ways with their star players, including the Belgian global, as they look to return to the top of English football. "I hope this can be a year of victory for us".