The Stamford Bridge number one has emerged as a potential target for the La Liga champions, with Jose Mourinho's side on the look-out for a replacement for Iker Casillas.
A question mark hangs over the future of the Spain international, after Casillas's very public falling out with Mourinho earlier this season.
Mourinho benched the Bernabeu legend in favour of back-up keeper Antonio Adan, prompting speculation the Spanish stopper could quit the club at the end of the season.
And the report claims Real Madrid are preparing contingency plans should that happen, with Cech one of many targets on their shortlist.
The 30-year-old keeper would not come cheap - he signed a four-year contract in May 2012 committing his future to the club until 2016 - and his new deal made him one of Chelsea's highest earners.
But the Daily Star carries quotes from Cech, taken from just before the Czech international signed his new Chelsea deal, which hinted at his willingness to try a new challenge away from Stamford Bridge some time in the future.
He said: "You never know, everything happens fast in football. You can sign a 10-year contract and then leave after three years. I'm 29 and believe there is still time for a possible change."
The former-Rennes keeper has been one of Chelsea's most consistent players since he joined the club in 2004 - he's won three Premier League titles, four FA Cups, two League Cups and one Champions League at Stamford Bridge.
Although a move for Cech would be a long-term solution to Mourinho's Casillas problem, Real Madrid have a short term issue at goalkeeper - Casillas is set to miss both legs of their Champions League last-16 tie against Manchester United with a broken hand.