Amakhosi played to a capacity crowd at the Mbombela Stadium last weekend during the 1-1 draw at Bidvest Wits, and Vermezovic is hopeful his side can start putting together the performances to draw the club's supporters to Soweto.
The Glamour Boys will have the chance to do just that this weekend when they host Cape Town All Stars in the Nedbank Cup, and the Serbian tactician is hoping his players give the fans something "to brag about".
"We want to see more fans coming to Soccer City on Saturday, we need to keep on playing an entertaining soccer and also win matches to attract more people to our games," Vermezovic told The Sowetan.
"The fans want entertainment and also to brag about the success of their club."
All Stars might sit two entire divisions below Chiefs, but defender Dominic Isaacs is aware that anything is possible when it comes to cup football.
"All Stars will be a difficult side because we know very little about them," said Isaacs. "They have a few players from Ajax Cape Town that I know from the era when I was still there. The players from Ajax played for the reserve side when I was still in Cape Town."
Isaacs' cautious approach to this weekend's encounter is largely down to Chiefs' shock quarter-final defeat to Baroka FC in last year's Nedbank Cup - a result the utility defender has pledged to avoid.
"Chiefs have not been doing well in this tournament in the past three seasons. We have been losing to amateur clubs, which we pledge to our fans will never happen again. We also want to win this tournament for the fans."