This is according to City club chairman John Comitis, who also admitted that they are looking to bring in a quality shot-stopper like Khuzwayo.
The 28-year-old, who is a highly-rated shot-stopper, is set to become a free agent at the end of June 2018 having failed to reach an agreement with Chiefs during contract renewal talks.
Khuzwayo served as an understudy to Chiefs captain and keeper Itumeleng Khune during his six-year spell with the Naturena-based outfit, and he has since decided to leave the Soweto giants in search regular game time elsewhere.
The Citizens were heavily linked with the former South Africa youth international during the January 2018 transfer window, but the Mother City side lost interest in the player as his demands were deemed unrealistic by Comitis.
The City boss was recently asked by The Citizen whether the club will consider making another move for Khuzwayo this winter.
“We discovered that his wage package is beyond our capacity and we did not pursue him,” Comitis told the publication.
City keeper Shuaib Walters has been linked with a move away from the Mother City side with his contract set to expire next month and the club is looking to bring in a new shot-stopper, who will serve as first-choice Sage Stephens' understudy.
Orlando Pirates and Highlands Park are the two clubs which are reportedly keen to snap up Khuzwayo ahead of the next Premier Soccer League (PSL) transfer window which is expected to open in July, 2018.
Khuzwayo made only three appearances in the league during the 2017/18 campaign.