Goalkeepers Steve Arnold (pictured) and Joel Dixon and former Premier League striker Grant Holt are all under contract for next season.
Those offered new deals for 2018/19 are Moussa Diarra, Nathan Waterston and Donovan Makoma.
Players who are under contract but made available for transfer by the Bluebirds are Asa Hall, Dan Jones, Jordan White, Bedsente Gomis and Jack Barthram.
And six others have been released and have left the Furness Building Society Stadium - Harry Panayiotou, Thierry Audel, David Fitzpatrick, Bradley Bauress, Tony Diagne and striker Byron Harrison.