The position will become vacant after the Nedbank Cup final between SuperSport and Orlando Pirates on the 24th of June 2017.
This is after Matsatsantsa agreed to release their current mentor Stuart Baxter, who was appointed Bafana Bafana head coach last month.
Former Orlando Pirates coaches Ruud Krol and Roger De Sa are amongst the tacticians, who have also been linked with the SuperSport hot seat.
According to MTNFootball, the race for the Matsatsantsa coaching job is over after they considered numerous candidates.
Tinkler, who is also a former Pirates coach, is said to have beaten De Sa and Krol to the position.
The Tshwane giants have invited the media to a formal announcement on Thursday afternoon.
Tinkler had a successful 2016/17 campaign at City - winning the 2016 Telkom KnockOut Cup and he also guided the team to a third place finish in the PSL.
It is said that the City management have agreed to release Tinkler, while De Sa has been tipped as his possible replacement.
De Sa has been jobless since leaving Maritzburg United three months ago.