Parker's contract with Kaizer Chiefs appears set to expire at the end of the season and it is yet to be confirmed whether or not the 36-year-old will be extending his stay at the club beyond the current campaign.
Amid speculation surrounding the former Bafana Bafana star's future, Amakhosi interim coach confirmed that the forward is interested in becoming a coach and backed him to succeed in a role on the touchline.
"I talk to each and every player and Bernard knows he won't play football forever," Zwane said post-match.
"He has hinted that he wants to take up coaching and I would advise him to apply for coaching courses. There are opportunities left, right and centre.
"I told him that he can go to Ireland as well. That's where I got my coaching license and he can also get help from SAFA and I think CAF will now allow the coaches because the situation with Covid is getting better.
"We will try and help Bernard. If he wants to do coaching, we will most definitely help him. We need more people who are influential, people who can lead by example.
"He's never been a troublesome player, he's always been disciplined. If he becomes a coach tomorrow, he will be a good leader."
Parker joined Chiefs from Dutch side FC Twente in 2011 and has since made more than 350 appearances for the club across all competitions.