The Belgium international has been heavily linked with a move away from Stamford Bridge in recent months.
Reports yesterday claimed the Chelsea star has agreed terms with Real Madrid ahead of his return to La Liga.
And according to TransferMarketWeb, new Blues boss Maurizio Sarri is eyeing Barcelona’s Cillessen as a replacement for Courtois.
They say the Blues are big admirers of the 29-year-old, who is set to leave the Nou Camp after two years at Barca.
Cillessen, 29, was tipped to join Liverpool before the Reds completed their world-record deal for Alisson.