Bischoff is not part of Stuart Pearce's plans although he said Bischoff would be welcomed back to the club for pre-season training after a proposed move to Wolves fell through.
City, however, were quick to accept Cardiff's undisclosed offer for the 23-year old who ended last season on loan at Molineux.
Despite joining Manchester City in 2002 Bischoff made just 1 league appearance for the club before two loan spells at Wolves last season where he went on to make 10 appearances in all competitions.