Valdes confirmed earlier this summer that he will not be extending his current contract at the Nou Camp which expires next year, meaning the Catalan club are on the lookout for a replacement.
They had previously been linked with a move for Liverpool goalkeeper Pepe Reina, who is now on loan with Napoli, amongst others, but according to the Mail they have identified Courtois as the right man for the job.
The Belgian international has been on loan at Atletico Madrid for the past two seasons but is viewed as the long-term successor to Petr Cech at Stamford Bridge.
The Mail claim Barcelona hope to play on the fact that Cech is unlikely to be moved from the number one spot at Chelsea for the foreseeable future.
A stumbling block could be that Chelsea are likely to value the 21-year-old at around £30 million, three times as much as the next man on their list, Borussia Monchengladbach's Marc-Andre ter Stegen.