As SA scrambles to contain a troubling outbreak in Adelaide, the attention of Victorian health officials has turned to ensuring it doesn't leak across the border.

A screening process was instituted on Monday for every SA arrival at Melbourne airport, with the names and details of 122 passengers recorded and 81 of them tested. None had visited a high-risk exposure site.

But Deputy Chief Health Officer Allen Cheng has opted not to impose a similar arrangement at border crossings into Victoria, noting traffic was already limited by current rules.

"No border restrictions have been imposed at this stage, but we are continuing to monitor the situation in South Australia," Professor Cheng said in a statement on Tuesday.

"All cases in the outbreak in South Australia have known links and are currently within metropolitan Adelaide, so the risk to Victoria's border communities is low.

"People in South Australia who have been at a high-risk location are required to quarantine, and the South Australian border is closed to most travellers from Victoria."

Just four days ago, SA announced it would reopen its border to Victoria on December 1.

Notwithstanding, Premier Daniel Andrews on Monday wouldn't rule out closing it from Victoria's side in future and nor did one of his ministers.

"I'm not making any presumptions here," Energy, Environment and Climate Change Minister Lily D'Ambrosio told reporters on Tuesday.

"I do want to reflect on the fact that Victorians have worked very hard and of course we don't want to put that in jeopardy.

"But, as we always have been, (we'll) be guided by the data, by the evidence and our health officials advice."

There were no scheduled flights from Adelaide into Melbourne or Mildura on Tuesday, but more were expected to touch down on Wednesday.

It came as Victoria's streak of no coronavirus deaths or new cases hit 18 days.

The number of active cases in the state remains at three as of Tuesday, as testing jumped dramatically from Monday's figure of 6695 to 17,412.

Victoria's virus death toll stands at 819, with the national figure 907.

Australian Associated Press