A potential post-Brexit trade deal with Australia could give Brits and Australians greater access to each other’s countries.
Currently, British citizens require a visa to travel to Australia and while Britons can apply for holiday working visas, they must go through normal channels to emigrate longer-term.
Speaking in Canberra on Wednesday, she said: “We want a fully comprehensive trade deal that reflects our deep, ongoing relationship, the friendship between our two countries, the fact that Australians want to come and live and work in Britain, and Brits want to come and live and work in Australia.”
Under the Trans-Tasman travel arrangement, there is a common travel area between Australia and New Zealand, meaning citizens from either country are free to travel, live and work in both.
However, Australian prime minister Scott Morrison dismissed the idea of expanding the scheme after a meeting with UK Prime Minister Boris Johnson at the G7 summit in France last month.
Morrison said at the time: “The New Zealand arrangement is quite unique and it’s not one we would probably ever contemplate extending.”
In efforts to reduce the economic impact of Brexit, Britain is looking to line-up a series of trade deals with smaller, non-EU countries.
“The reason that I have chosen to make Australia one of the first countries I have visited as trade secretary is because it is an absolute priority to get on with this trade deal,” Truss told reporters in Canberra.
“I would say months rather than years for it to be completed.”
But parliament this month passed a law that requires Johnson to ask the EU for a three-month delay to Brexit if a deal is not approved by October 19.
Two-way trade between Australia and Britain is worth A$26.6 billion (£14.64 billion), data shows. The UK is Australia’s seventh-largest trading partner.
Australia’s Minister for Trade Simon Birmingham said a trade deal with Britain will particularly benefit the country’s agricultural sector, worth around £32.95 billion.
“As part of the EU, market access to Britain in terms of agricultural products has been limited,” Birmingham told reporters. “This is something we will look to address.”
CORRECTION: An earlier version of this article stated freedom of movement was currently bering discussed. Liz Truss actually said freedom of movement could form part of future trade negotiations.