The very few Australians allowed to fly into the United Kingdom could be excused from spending 14 days in quarantine.
Trade Minister Simon Birmingham discussed the quarantine exemption with his British counterpart this week.
He said the potential exemption was more likely to benefit Brits trying to return home than Australians travelling to the UK, unless they had exceptional circumstances.
The only travel allowed out of Australia is for compassionate or essential reasons so a British holiday or business trip is out of the equation.
Australia argues its success in bringing the disease under control at home makes it a low-risk country abroad.
Several UK cabinet ministers support the exemption idea but others do not want to complicate the system.
"We welcome any recognition that Australia has led the world in the successful containment of COVID-19, which clearly means that travellers coming from Australia would pose a low risk to the rest of the world," Senator Birmingham told AAP on Friday.
"However, transmission from overseas continues to present a risk to Australia's ongoing suppression of COVID-19 and restrictions on travel in and out of Australia will remain for the foreseeable future."
But Senator Birmingham's message to anyone planning a quick British trip was blunt: "I'd pretty much say forget about it for a while."
The UK quarantine regime is expected to start next month.
Australia's international borders have been shut since March 26 and will not reopen anytime soon.
Overseas travel is effectively banned and people trickling into the country are being forced to spend two weeks in hotel quarantine.
Australian Associated Press