Blues are in need of a reserve goalkeeper for next season.
Chelsea are set to return with an improved offer of £10 million for Norwich City keeper John Ruddy, says the Daily Mail.
The west London club are currently on the look-out for a new No 2 to provide cover for first-choice goalkeeper Petr Cech at Stamford Bridge next season now that their previous back-up shot-stopper Ross Turnbull has left the club.
And new Blues head coach Jose Mourinho is understood to see the England international as being the ideal man to take on the role in the capital next season, so much so that the club are prepared to double their original offer of £5m in order to secure the 26-year-old custodian this summer.
Ruddy has been at Carrow Road for the past three years now having originally arrived in East Anglia from Everton, and last season made his England debut in a friendly against Italy in Switzerland on the back of what was an outstanding campaign between the sticks for the Cannaries in which Ruddy kept five clean sheets in his 10 top-flight appearances for the strugglers.