According to Sportswire, Tinkler arrived in Durban on Tuesday as he prepares to replace Khalil Ben Youssef, who was dismissed following a difficult start to the season.
Tinkler recently resigned as head coach of Ghanaian giants Asante Kotoko after just four matches in charge, informing his players that he had received an opportunity to return to South Africa.
The former Bafana Bafana midfielder had previously spoken positively about his experience in Ghana after taking charge in July, but negotiations with Durban City had reportedly been ongoing for more than a week before he decided to leave Kotoko.
Durban City have yet to officially confirm Tinkler's appointment.
Sportswire contacted club chairman Farook Kadodia for comment regarding Tinkler's reported arrival, but he did not directly address the coach's situation.
"The club is going through a difficult time, both in terms of on-field performance and coaching stability. There were irresponsible statements made by certain media outlets on Saturday, and we need to protect our brand. Please give us time before we put corrective measures in place," Kadodia said.
Ben Youssef was appointed during the off-season after leaving Kaizer Chiefs at the end of last season. The Durban City job was his first as a head coach.
Tinkler, meanwhile, brings extensive PSL experience, having previously managed Orlando Pirates and Cape Town City, as well as Maritzburg United.
His reported return to Durban would also reunite him with Kadodia. Tinkler was appointed Maritzburg United coach in January 2019 and helped the club recover from a difficult position to finish seventh that season.
He subsequently guided the team to the Carling Knockout final, where they lost to Mamelodi Sundowns, before being dismissed in November 2020 following seven consecutive defeats.
Tinkler would inherit a Durban City side sitting 10th on the PSL log with seven points from seven matches.
His CAF A Licence is also understood to have played a role in the club's decision, with Durban City preparing for their CAF Confederation Cup second preliminary-round campaign.
Tinkler's first reported match in charge would come against AmaZulu at Chatsworth Stadium on October 13, with the coach facing the immediate task of stabilising the club's fortunes.