Under Benni McCarthy, the club made history by qualifying for the CAF Champions League in 2021/22 and reaching the group stage.
Their only top-flight title to date remains the 1992 Coca-Cola Cup where they beat Kaizer Chiefs 3-1 in the final, and Zwane is eager to replicate that success.
First up is a last 32 clash with Betway Premiership rivals Polokwane City, who they face at the Old Peter Mokaba Stadium on Tuesday.
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Speaking ahead of the game, Zwane explained his lofty ambitions with his team sitting in an impressive fourth place on the Betway Premiership standings with 30 points from 17 games – five adrift of league leaders Mamelodi Sundowns but from two games more.
“We need to go all the way in the Nedbank Cup,” Zwane said. “Like any other team that wants to compete against the best, we’d like to see ourselves in the final. Hopefully we can do what was done by the generation of 1992.
“It was a quality team, the Joseph Mlabas and Simon Magagulas of this world. Funny enough, I shared the room with Magagula at Pirates. It was a quality side AmaZulu had assembled in 1992, and we just want to emulate that team.”
“We also want to use the Nedbank Cup as a ticket to play continental football next season because it’s important for our players to compete at that level,” Zwane added.
“We’ve competed in the Champions League before, so we want to return to that space, and we really fancy our chances, given the fact that our position is good.”