The state government is due to announce its plans for the new school year later this week with health officials previously conceding there will likely be some disruptions.
Chief Public Health Officer Nicola Spurrier told a parliamentary committee on Monday that SA Health was looking at RAT surveillance for teachers.
But she indicated that was unlikely to be extended to students at this stage, despite the fact that most primary school children would not be fully vaccinated by the scheduled start date of January 31.
"We would need to have a look have at the supply and we need to focus our resources on what is the best bang for our buck," Professor Spurrier said.
"The people who are at highest risk in our particular environment are people with symptoms and those who are close contacts."
The committee was also told that while SA had about 144,000 children aged between five and 11 who were still to be vaccinated, Health SA would receive only about 70,000 doses during January.
Although that number would be bolstered doses to be provided through GPs and pharmacies, with the first doses allowed across both sectors from Monday.
The vaccination rate for primary school children would be one of a number of factors to be considered in the state's return to school strategy, along with the wider use of masks and specific contact tracing arrangements.
"We'll be strongly supporting the use of masks in schools," Prof Spurrier said.
SA reported a record 4506 new virus cases on Sunday with 27,762 active infections.
Figures for Monday are yet to be announced.
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