Singh secured a R25-million transfer from SC Braga to the Danish Superliga giants in August and signed a four-year contract with the club Zuma forged an iconic status with between 2000 and 2005.
While excitement has brewed over his move to the club, there has been notable criticism directed at his recent displays in national team colours. But Zuma feels the move to Scandanavia will soon propel him to the next level for club and country.
"Copenhagen called me when they were looking at him and asked me what I thought and I said he reminds me of myself, he still has a lot to learn but he's going to get better there," Zuma told snl24.com/kickoff.
"I was not ready when I left South Africa as well. The boy is fast, he can score goals, is very tricky and enjoys one against one, Danish football loves that and the South African way of playing.
"So if our youngsters can get into that level, take the speed seriously, take on players and score goals, they can end up in Copenhagen like him. They must just take the game seriously and work hard with extra training."
He added: "One thing I promise you is that he is going to be a different player for South Africa when he comes back to represent the country because I know the quality physical trainers there, so he's going to improve big time.
"That's the reason I'm always saying our PSL players need to try and make these moves to overseas teams, improve and come back to help the national team. Look at him when he comes back next, he'll be a different player."
The 24-year-old has made three substitute appearances for his new club since his arrival and is expected to make his full debut when they return to league action against Randers on Sunday.