The 31-year-old has a wealth of experience in the second tier and was part of the Bluebirds' squad between 2004 and 2006 before moving on to stints with Birmingham City, Stoke City and the Canaries.
Jerome is no longer thought to be part of Norwich boss Daniel Farke's plans, however, and has made just two appearances from the bench in the last eight weeks.
According to The Mirror, Cardiff manager Neil Warnock has been monitoring Jerome's situation and sees him "as an ideal target man to improve their attacking options".
The Welsh side are currently third in the Championship table and have been promised a "reasonable" transfer kitty by owner Vincent Tan in order to aid their promotion push in the second half of the campaign.
Jerome, whose current contract at Carrow Road expires in 2019, is also said to be of interest to fellow promotion-chasers Derby County.