The Canaries turned down a £5million offer from the Europa League winners last week, with the Norfolk club holding out for a fee closer to the £10million mark for the England international.
Jose Mourinho has been on the lookout for a backup for first choice Petr Cech following the releases of Ross Turnbull and Hilario, while Belgian international Thibaut Courtois has been allowed to extend his loan with Atletico Madrid for a third year.
Ruddy has impressed for Norwich since their return to the top flight two years ago, earning his first international call up in a 2-1 friendly win over Italy last August, though he missed a large part of the 2012/13 campaign with a thigh injury.
The 26 year old began his career with Cambridge United before being transferred to Everton in 2005, though he made just one substitute appearance in five years with the Toffees.
Ruddy was loaned out to no fewer than nine clubs during that time, spending a year with Motherwell in the Scottish Premier League just before his transfer to Carrow Road in 2010.