The move could speed up the turnaround for results.

Wangaratta hospital director David Kidd outlined that scenario on Tuesday following the first day of operation for a specialist COVID-19 screening clinic in his city.

There were 35 patients seen and 22 tested after a prior phone assessment.

"That's not a surprising number for the first day, we're expecting probably double that in coming days," Mr Kidd said.

Those attending included travellers returned from overseas, health professionals and the elderly.

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They are expected to have their results by Thursday.

A drive-through clinic will begin testing for coronavirus in Wodonga on Wednesday.

It has been established by Albury Wodonga Health and like its Wangaratta counterpart, patients will need to have received a referral to have a screening at the clinic.

Albury Wodonga Health's director pandemic response Sally Squire said it would initially operate during business hours but may increase its opening times.

She said although calls to the hospital from concerned citizens were rising, few ultimately require testing.

"It's actually quite a small percentage of our patients that actually call up for the testing that actually go on to have the test," Mrs Squire said.

"We're beginning to see the cold and flu season too so people are probably beginning to see little colds and flus and they want some assurance that that's not something more serious."

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Mrs Squire said the service's hospitals were prepared for what she flagged could happen.

"The world is a small place and people move around and there is a very real likelihood that we may see cases here, but I want to assure people that we are very well prepared," Mrs Squire said.

"Our staff are prepared, we're prepared with equipment and I think that we're taking this very seriously and we want to make sure that the public feel assured that we've got measures in place."

Mrs Squire said there had been no COVID-19 cases found on the Border and if there was one the public would be notified.

She said that would involve outlining movements of the coronavirus carrier and alerting the community.

"Contact tracing is part of what we would do, if there was a positive case we would certainly be investigating that," Mrs Squire said.

With Facebook users making claims about coronavirus in the region, Mrs Squire urged people to rely on authoritative founts.

"There's a lot of things that come out in the media and particularly social media that may not be fact, so I would really encourage people to go to reliable and credible sources," Mrs Squire said.

"(Those) that gives them good information to make decisions about their own health and if in doubt please contact your GP or contact us here at the hospital."

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