The Citizens were hoping to sign the Umlazi-born shot-stopper before the current transfer window slams shut early next month, or even better, sign him on a pre-contract for the 2018/19 PSL season.
According to City boss John Comitis, Khuzwayo's camp, led by Tim Sukazi, has already made demands that are unrealistic in the early stages of the negotiations.
"Yes, we want to sign Khuzwayo and we’ve already engaged his agent, but his demands are unrealistic," Comitis told Independent Media.
"The numbers they are asking for are unaffordable," Comitis explained.
The 27-year-old, who is in the final six months of his contract with Amakhosi, told his current employers to guarantee him some game time before he can sign a new deal.
At this stage, it looks like Khuzwayo will be stuck at Naturena for the remainder of the season, and chances are that he could be frozen out should he turn down the club's offer.
In 2013, Lehlohonolo Majoro found himself training on his own after rejecting a new Chiefs deal. He later joined Orlando Pirates on a free transfer.