Free movement between Australia and the UK would be explored by the government in “post-Brexit” business talks, Liz Truss, the international trade secretary, has announced.

Yesterday, while on a trip to Australia, Truss told journalists in Canberra that securing a trade deal was an “absolute priority” after Britain left the EU. She believed an arrangement would take months rather than years to complete.

The proposal, which would allow British citizens to live and work in Australia visa-free, and vice-versa, was part of ongoing trade talks, she said.

At a press conference with the Australian trade minister, Simon Birmingham, Truss was asked about a freedom of movement proposal.

She said: “We’ve been clear on the fact we want to adopt the Australian-based points system in terms of our new immigration system as we leave the European union. We’ve recently made an announcement that we’re extending the work period after foreign students come to the UK for two years.

“But of course, our two countries have a special link and a historic relationship, and it’s certainly something that we will be looking at as part of our free-trade negotiations.”

Britain is Australia’s seventh-largest trading partner, and the value of two-way trade is said to be worth up to $26.6bn (£14.60bn).

Birmingham said a trade deal with Britain would particularly benefit the UK’s agricultural sector. However there could be concerns about the proposal in Australia, as well as in New Zealand, which currently has visa-free arrangement with the country.

Australia’s prime minister, Scott Morrison, said recently the Trans-Tasman visa-free arrangement with New Zealand was unique and not something his government would consider extending to other countries.

In New Zealand potential free movement to the UK could spark deep concern about a repeat of the “brain drain” in the early 2000s when skilled workers left the country in their thousands.

Truss said the UK and Australia were “old friends, with new opportunities”. She was also due to be going to Japan for trade discussions.