Chelsea are considering returning to Norwich City with an improved offer for their England goalkeeper, John Ruddy, having had an initial bid for the player rejected.

The Europa League winners are seeking a back-up goalkeeper for Petr Cech and would ideally like to sign an Englishman with an eye on homegrown numbers for European competition. Ross Turnbull, who filled the role last season, has been released with Chelsea having sought to secure Jack Butland in January – the player eventually left Birmingham City for Stoke – and considered Fraser Forster at Celtic.

Their move for Ruddy saw an offer worth an initial £3m, with a further £2m of add-ons, tabled earlier this week only for Norwich – whose players report back for pre-season training on Thursday – to reject the approach and insist the 26-year-old is not for sale. That resolve may yet be tested with Chelsea expected to return with a new offer, potentially with more of the fee to be paid up front.

The London club's third-choice goalkeeper, the Portuguese Hilário, was out of contract at the end of last season but is likely to sign a new 12-month deal at Stamford Bridge to remain No3, with the youngster Jamal Blackman also highly rated by the goalkeeping coach, Christophe Lollichon.

Chelsea, who have loaned Cech's long-term successor Thibault Courtois back to Atlético Madrid for the season ahead, are expected to send their young French forward Gaël Kakuta back to Vitesse Arnhem on loan for the campaign.