Chelsea face a battle to hold onto Courtois who has been a long-standing target for Real Madrid.
Courtois has yet to commit his future to the west London outfit which remains a big concern.
Reports earlier this week suggested Real are hoping to land Courtois and his Blues team-mate Eden Hazard for a combined £150million.
Maurizio Sarri is currently shaking up his squad, although Courtois is one of four players he has no desire to see leave before the transfer window closes on August 9.
However, with the possibility that the Belgian could head for the exit door, Sarri is drawing up a short list of potential replacements.
And according to The Sun, Chelsea are considering a surprise swoop for Manchester City goalkeeper Hart.
It is said that Hart, who would cost around £5m, is admired by the Blues hierarchy and would also boost their count of homegrown stars.
However, such a move could risk riling the fans as the 31-year-old failed to hold down the No 1 spot on loan at West Ham last term and was left out of England’s World Cup squad.
Hart, who spent the season before on loan at Torino, has been told he has no future at the Etihad under Pep Guardiola.
With just 12 months left to run on his contract, City have to decide whether to sell him now or risk losing him for free next summer.
City are currently on pre-season tour of the US where they are involved in the International Champions Cup.