With Hilario and Ross Turnbull released by the Europa League winners and Thibaut Courtois given the green light to spend a third season on loan at Atletico Madrid, Petr Cech and young Sam Walker are the only remaining stoppers at Stamford Bridge.
Jose Mourinho is believed to want Ruddy to provide competition for veteran Cech, but after having a reported £5m bid rejected last week, various sources say a £7m offer has now also been turned down by the Canaries.
Norwich are believed to be holding out for £10m for the 26-year-old, despite Chelsea’s reluctance to spend huge with one eye on Financial Fair Play regulations.
Ruddy joined Norwich from Everton in 2010 after being loaned out to no less than eight different clubs from Goodison Park, including two spells at Stockport County.
He earned his one and only England cap to date as a half-time substitute in the 2-1 friendly victory over Italy on August 10 of last year, having pulled out of his Euro 2012 call-up with a broken finger.
Meanwhile, West Brom confirmed they had turned down an offer from Chelsea for their teenage midfielder Isaiah Brown.Brown, 16, made his debut for the midlands outfit last season, coming off the bench in the 3-2 Barclays Premier League home loss to Wigan in May - his sole senior appearance to date. He has been capped by England at Under-16 and Under-17 level.
A statement on West Brom's official website said: "Albion have today rejected an offer from Chelsea for academy product Isaiah Brown. Under Premier League rules the Baggies are due compensation from the London club for the 16-year-old midfielder, who has been at the Hawthorns for three years and had agreed to sign scholarship forms."
Albion sporting and technical director Richard Garlick said: "We are disappointed by Chelsea's offer.
"We have invested a lot of time and money in Isaiah's development as a player and - as one of our most exciting academy products in recent years - we had hoped to bring him through into our first team.
"But Chelsea have forced our hands and we are more than prepared for the matter to be decided by a tribunal if needs be.
"More importantly, it makes you question why these young players are joining bigger clubs when they are likely to gain more first-team opportunities in the Barclays Premier League at clubs similar to us."