Real Madrid have reportedly resolved to make their final decision on a new goalkeeper by the end of the month.
Courtois has 18 months remaining on his contract at Stamford Bridge, leaving the Blues needing to extend the Belgian stopper's deal or risk losing him on a free transfer in 2019.
Real are also interested in Athletic Bilbao's Kepa Arrizabalaga and it has already been suggested that Zinedine Zidane has plans in place to sign the young Spaniard either in January or in the summer.
According to The Sun, Real will finalise their plans between the sticks by the end of 2017, leaving Chelsea and Athletic both awaiting an official approach.
Keylor Navas is currently regarded as Real's number one, but the arrival of either Courtois or Arrizabalaga would throw the 30-year-old's future into doubt.