Premier Steven Marshall says the government just needs a "few more days" before it makes the call based on the number of people lining up for their second jab.

"We just need a few more days to see what that run rate is going to be in South Australia," he told reporters on Thursday.

"The race is on at the moment to get to 90 per cent of all those 12 and over and I'm hopeful that we can do that by the end of the year."

The most recent SA Health forecast suggests the double-dose target would be reached between December 23 and January 3.

Among the measures that could be revised are density limits at various venues, restrictions on dancing in nightclubs, and the 150-person cap on private functions.

SA currently has 51 active COVID-19 infections with seven new cases reported on Thursday.

Two of those were linked to the so-called Norwood cluster, taking it to 30.

The five others included four people who acquired the infection interstate before arriving in SA and one was a returned overseas traveller.

All SA's cases are being managed in hotel quarantine apart from a woman in her 50s and a man in his 60s who remain in the Royal Adelaide Hospital in a stable condition.

Meanwhile, a case detected in Adelaide on Wednesday has forced the closure of the Our Lady Queen of Peace School at suburban Albert Park.

The school said a positive test was returned by a member of the school community.

It said while classes had finished for the year the site was being cleaned, with SA Health working to determine any close contacts as well as those considered casual contacts.

Some students who attended the school on Monday and Tuesday are required to get tested and quarantine, along with year six pupils and parents who attended a graduation ceremony on Monday night.

"Please be assured that we will be closely following the advice of SA Health," the school said in a Facebook post.

Australian Associated Press