Mr Turnbull has met 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.
