The 22-year-old has barely featured in the first team at City since moving from Denmark in 2002 but impressed on a loan spell at Wolves last season.
Then boss Dave Jones is now with Cardiff and after selling Welsh internationals Danny Gabbidon and James Collins to West Ham this week for a fee of £3m, Jones is hoping to get City's young Dane in to fill the void in
central defence.
The Bluebirds are believed to want a loan deal but City boss Stuart Pearce, who said at the start of the summer he would give Bischoff a chance to prove himself in pre-season training, is willing to be flexible.
Bischoff has suffered badly through long-term injury and the emergence of teenager Nedum Onuoha while Sylvain Distin and Richard Dunne have formed a solid partnership at the back.