The tactician served as the Pirates head coach during the 2015/16 season and the Soweto giants finished as runners-up in the Caf Confederation Cup and Nedbank Cup under his guidance.
Khoza recently stated that he was not keen on losing Tinkler, who parted ways with the Buccaneers at the end of the campaign having joined the club as Roger De Sa's assistant in 2012.
“My relationship with the chairman has always been very, very strong,” Tinkler was quoted on The Star.
“It goes all the way back to my playing days at Bafana Bafana. I am very proud of what he has gone and said to the public," he continued.
Tinkler also worked as Vladmir Vermezovic's assist at Pirates between February and December 2014.
"But I pride myself in that any club that I have represented or coached can never have a bad thing to say about me because of who I am as a person and how I apply myself as a professional," he added.
"Nobody can ever point an accusing finger at me (and say that I didn’t give my all). It doesn’t surprise me that the chairman would say that," he concluded.
After leaving Pirates, Tinkler joined newly established Cape Town City ahead of the 2016/17 season and he won the 2016 Telkom Knockout Cup with Mother City side.
But the former Bidvest Wits assistant coach left the Citizens for SuperSport prior to the current season and he will face City in the 2017 MTN8 Cup final on Saturday.
SuperSport are also in this year's Confederation Cup semi-finals having drawn 1-1 with Tunisian giants Club Africain in the first-leg match in Pretoria two weeks ago.
The second-leg clash will take place at the Stade Olympique de Radès in Radès, Tunisia on Sunday, October 22.