SA Health says two men in their 50s have tested positive for the virus after attending the same event as interstate travellers.

"While the cases are currently under investigation, we believe the virus was passed on from an interstate traveller at the event," it said in a statement on Wednesday.

A number of exposure sites linked to the two cases included a theatre venue in suburban Norwood, a seafood restaurant, a cafe in Adelaide's CBD and the Business SA headquarters in Unley.

Media reports said former SA premier Jay Weatherill, who now lives in Western Australia, was at the same event as the positive cases

If so, he is likely to need to quarantine for seven days.

Anyone who attended the event and was unvaccinated is required to quarantine for 14 days.

A child who recently returned from overseas has also tested positive for the virus, taking the number of active infections in SA to nine.

There have been 13 cases since the border rules were relaxed on November 23.

Other than the two men on Wednesday, all involved interstate or overseas travellers.

Under current arrangements, SA is open to vaccinated travellers from all states and territories, with some requirements for testing and quarantine.

International arrivals are required to quarantine for 14 days, regardless of where they come from.

Local restrictions, such as mandatory mask-wearing on public transport and in most venues, also remain.

The state's transition committee met on Tuesday but left all travel and local restrictions unchanged despite concerns over the new Omicron variant of the virus.

Premier Steven Marshall said previously there was an "inevitability" about cases in South Australia under the new border rules.

"But what we want to do is to get to those cases as early as possible," he said.

"So that we're minimising the number of people who need to have testing or potentially go into isolation."

Australian Associated Press