The 33-year-old is likely to leave the Brazilians as a free agent this winter with his current deal with the club due to expire at the end of next month.
Nthethe, who joined Sundowns from Celtic midway through the 2013/14 season, has fallen out-of-favour at the Chloorkop-based side having made only one appearance in the PSL this season.
Top PSL sides SuperSport United and Orlando Pirates were linked with 'Mr Cool' prior to the January 2018 transfer window, but the player stayed put in Chloorkop.
The latest reports have since revealed that City head coach Benni McCarthy is a big fan of the central defender, who was nurtured in the Celtic academy.
“Benni rates Nthethe highly," the Daily Sun source said about the ageing defender.
City club chairman John Comitis has reportedly opened talks with Nthethe, who can negotiate with any club interested in his services as he is in his final six months of his Sundowns contract.
"He jumped at the chance to try and lure him to his stable when he noticed that Nthethe was not getting a run at Sundowns," the source continued.
"He also asked Comitis to start negotiations early, which shows he wants to build his defence around Nthethe next season," the source revealed.
On the other hand, Celtic are said to be ready to offer Nthethe a position on their technical team once he retires from professional football.
“Celtic plan to add him to their technical setup when he retires, if he takes up the offer,” the source added.
Nthethe, who was born in Bloemfontein, helped Phunya Sele Sele win the 2012 Telkom Knockout Cup as the club captain.