Last week the Citizens were fined for failing to obtain prior approval from the Premier Soccer League executive committee before donning a new kit with the logo of their new sponsor.
City were fined R50 000, though half of it was suspended for a period of 24 months on the condition that they are not found guilty of the same offence.
In an almost identical incident in 2021, the PSL intervened and rejected Swallows' deal with Telkom as a shirt sponsor.
"Whatever is happening with the league and Cape Town City it's for Cape Town but we're busy trying to get a sponsor wherever we can.
"That's all we want and don't want to get involved," Swallows FC CEO Sipho Xulu tells KickOff.
"We are going ahead with our search for new sponsorship.
"What I can tell you is we are on a hunt for a new shirt sponsor.
"At Swallows, we don't compare our issues with other people's issues.
"The official statement from the club is that the club is not comparing its matters to other people's matters.
"There's this song sang by Kings Star Brothers saying 'Asishayi ingoma yomuntu ngoba sisaba amacala."