Reports emerged on Wednesday afternoon that the 46-year-old had already said his goodbyes to the Mother City outfit, fueling speculation that he could on his way to SuperSport United.
Tinkler, who signed a three-year contract with City at the start of last season, helped the club finish third on the log in his first season.
He also delivered the 2016/17 Telkom Knockout Cup in December 2016, beating Matsatsantsa in the final.
Cape Town City revealed in their statement that they will announce Tinkler's successor within the next seven days.
Roger de Sa and Muhsin Ertugral are already linked with the vacant coaching position at City, while Tinkler is expected to be unveiled as the coach for Matsatsantsa in a press conference on Thursday afternoon.
SuperSport lost Stuart Baxter to Bafana Bafana in May, and have been working around the clock to find a suitable replacement.
Kaitano Tembo has been in charge of the first team in the Caf Confederation Cup, as Baxter was unable to travel with the club around the continent.