Speaking during a visit to Canberra, Ms Truss said that free movement for Australian nationals would “certainly” be looked at as part of negotiations on a new trade deal.
Home secretary Priti Patel was forced to back away from plans to end EU citizens’ rights to settle and work in the UK immediately if a no-deal Brexit goes ahead on 31 October.
But EU nationals resident in the UK are being told to apply for settled status by the end of 2020 in order to be able to remain without a visa.
At a press conference with Australian trade minister Simon Birmingham, Ms Truss was asked about a possible freedom of movement proposal.
According to reports in the Australian press, she replied: “It’s certainly something we will be looking at as part of our free trade negotiations.”
Ms Truss 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.
“Leaving the European Union really does give us a chance as a country to become more outward-looking, to become more competitive, and to deepen our links with our partners right across the world.
“The reason that I’ve chosen to make Australia one of the first countries I’ve visited as trade secretary is this is an absolute priority for me to get on with this trade deal.”
There was no immediate response from the Department for International Trade, the Home Office or Downing Street to Ms Truss’s comments.