This comes after City boss John Comitis confirmed that the 26-year-old will not be sold to a local club in the current transfer window.
Comitis recently rejected an official bid from an unnamed Turkish club, although it is unclear at this stage if the European club will return with an improved offer.
Amakhosi are desperate to sign a quality striker before the transfer window closes on Thursday, but with Mamelodi Sundowns also in the picture, it remains to be seen if the Soweto giants will meet City's asking price for Manyama.
They will have to prepared to folk out no less than R10 million for the services of Manyama should Comitis change his mind about keeping the player for the foreseeable future.
In 2013, Manyama turned down the opportunity to join Chiefs despite his then club, Ajax Cape Town, agreeing a transfer fee for the forward.
Instead, Manyama moved to SuperSport United where he had an unsuccessful spell before joining Mpumalanga Black Aces.
The Glamour Boys have been criticized for not spending enough money on quality players in recent years, and their attempt to sign Manyama will certainly raise a few eyebrows among their fans.