Peter Ridsdale has confirmed that Norwich have accepted City's offer for the former Celtic player.
Marshall made 50 appearances for Celtic and has two Scottish caps.
It's said he's now to travel toCcardiff for a medical and to discuss personal terms.
The 24 year old is seto compete with Peter Enckelman for the No.1 shirt next season.
Marshall's claim to fame so far has been saving a penalty from Ronaldinho in the Champions League for Celtic.