The Canaries, back in the Championship again after a season in League One, have already signed Elliott Ward and are being reported as being interested in taking the former England U21 international defender.
Cranie, who played the last 29 minutes of the pre-season game at Nuneaton on Wednesday, was played in a number of positions by the then City manager Chris Coleman last season after joining the Sky Blues in August 2009.
He has made 38 league starts for City plus two substitute appearances, scoring one goal and two appearances in the FA Cup.