Mr Turnbull will meet Mrs May on the sidelines of the G20 summit in the eastern Chinese city of Hangzhou on Monday morning.
Mrs May has told the British press she would like Australia to be one of the first nations that Britain does a trade deal with to show it’s “open for business,” despite Britons voting in June to leave the world’s biggest single market - the European Union.
When asked about her desires, Mr Turnbull replied that “we are on a unity ticket with that”.
“We are already well advanced. We have got things moving towards having a free trade agreement with the UK,” Mr Turnbull told Australian journalists travelling with him in Hangzhou.
“Britain, when it exits the EU, which is obviously not going to happen tomorrow, it will take several years, but they have got to put in place the free trade agreements and we enthusiastic and supportive.”
Mr Turnbull also confirmed that Australia, along with New Zealand and Canada, were lending Britain specialist trade negotiators, because the UK doesn’t have any.
“You’ve got to remember Britain has not negotiated a trade agreement for a long time - they’ve been a part of the EU,” Mr Turnbull said.
The British newspaper the Daily Telegraph says these specialist negotiators will be “critical to Britain’s hopes of striking a good exit deal from the EU in Brussels, as well as forging fresh trade pacts with other countries around the world.”
When Mrs May and Mr Turnbull meet, they may spend a few minutes reminiscing about their university days, the pair were at Oxford at the same time.
Mr Turnbull appears to be enjoying his time on the world stage, leaving behind a messy first week of the new parliament, where his government lost three votes on the floor of the House of Representatives, the first time that’s happened to a majority government since the 1960s.
The topic of Brexit dominated Mr Turnbull’s discussions with German Chancellor Angela Merkel on Sunday afternoon. He re-iterated that Australia, despite wanting to do a deal with Britain – was still keen to pursue a free trade agreement with the EU.
He’s also had bilateral talks with leaders of the world’s two most populous nations, China’s President Xi Jingping and India’s Prime Minister Narendra Modi.
G20 wraps up with action on economy
Malcolm Turnbull and other G20 leaders are set to endorse a new set of rules to guide cross-border investment and new ways to help the world's poorest nations.
The G20 summit in the eastern Chinese city of Hangzhou will wrap up on Monday afternoon with the final communique released by host, President Xi Jinping.
It is understood the leaders will approve guidelines for governments working on reforming their cross-border investment policies, amid growing concerns populist parties are pressuring nations to economically "hide under the doona", as Mr Turnbull described it on Sunday.
The principles, which will be non-binding, will "help foster an open, transparent" global environment for investment, according to officials close to the talks.
The leaders will also endorse a plan to help developing countries, especially in Africa, lift themselves out of poverty over the next decade and a half.
Mr Turnbull will meet with French President Francois Hollande, as Australia seeks to seal a trade agreement with the EU and works with France to deliver new submarines.
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An overarching theme of the final communique will be committing all G20 members to monetary, fiscal and structural reforms to achieve solid and sustainable growth.
Under pressure from Europe, the United States and Australia, there is also expected to be a statement on excess capacity in the steel industry which requires "collective responses".
Mr Turnbull believes the overproduction and dumping of cheap steel is threatening the viability of the industry in Australia.
European Commission president Jean-Claude Juncker said on Sunday China must set up a mechanism to address its problem of industrial overcapacity, saying it was "unacceptable" the European steel industry had lost so many jobs in recent years.
"Overcapacity is a global problem but there is a particular Chinese element," he said.
China produces half the world's 1.6 billion tonnes of steel and has struggled to decrease its estimated 300 million tonne overcapacity, and rising prices have given companies there an incentive to boost production for export.
President Xi says he wants the summit to move from being one dealing with crises to long-term economic leadership.
"The G20 should fully honour its commitments," he told the opening session.
The leaders held a working dinner on Sunday night followed by a grand gala directed by Zhang Yimou, the film director responsible for the opening ceremony of the Beijing 2008 Olympics.
With AAP
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