A total of four new infections have been reported in Victoria on Tuesday, including one case in hotel quarantine.

The new cases came from 32,544 tests, a marginal increase from Monday's figure with wait times reducing significantly as testing capacity ramped up further.

The state's number of active cases stands at 38.

Victorian health authorities are confident the Black Rock coronavirus cluster is on a "very positive trajectory".

So far 24 cases have been directly linked to the outbreak, all connected to the Buffalo Smile Thai restaurant in bayside Melbourne and linked back to a cluster in NSW.

Testing commander Jeroen Weimar said at the day four mark of the outbreak on Monday they're at the point they'd want to be with identifying cases and close contacts.

More than 1000 primary and secondary contacts are isolating and a growing number of exposure sites have been identified.

The latest include a Boost Juice at Chadstone, a Puffing Billy railway stop in Emerald, a Keysborough Sikh temple and the Grape and Grain Cellars in Moorabbin.Mr Weimar said the goalposts for the virus kept shifting.

"They moved radically on New Year's Eve when we saw the virus imported from NSW here in Victoria at Black Rock," Mr Weimar said."We can't just ignore that and say we don't want to play by the rules we've always had.

"Close contacts, anyone who has been at exposure sites and 60,000 returned travellers flocking for testing have caused strain on facilities.

The daily update comes as a stranded family with a disabled child and another with special needs remain among the thousands of Victorians seeking an exemption to return from NSW.

More than 2300 applications have been made for exemptions to cross the NSW border after it slammed shut on Friday night, with only 175 processed on Sunday.

Testing commander Jeroen Weimar said medical exemptions are being processed quickly but others are taking 24 to 48 hours.

Former federal Labor leader Bill Shorten has revealed a family stuck on the NSW south coast contacted him in a bid to expedite their border exemption.

"I've been dealing with a constituent of mine," Mr Shorten told Nine's Today.

"Her and her husband they've got a disabled child and another child with special needs.

"Far better to have this child, this 11-year-old, looked (after) at home, rather than stuck in south coast NSW."

The former federal opposition leader said he would be "hitting the phones" on Tuesday to ensure their exemption was sorted out.

He said the exemption system "doesn't seem to be working the way it should" and implored Victoria's health department to speed up the assessment process.

"Let's just get it done quickly," Mr Shorten said.

"A whole lot of Victorians on holiday (have been) caught off guard, no chance to sort this out.

"We need now the administrative follow-up to help make sure people are not stranded in some really tough circumstances, like the lady I'm talking about."

Victorian health authorities are confident the Black Rock coronavirus cluster is on a "very positive trajectory".

As of Monday, 24 cases were directly linked to the outbreak - all connected to the Buffalo Smile Thai restaurant in bayside Melbourne and linked back to a cluster in NSW.

More than 1000 primary and secondary contacts are isolating and a growing number of exposure sites have been identified.