Senator Farrell revealed he extended the invitation for South Korea to apply for entry to the Comprehensive and Progressive Agreement for Trans-Pacific Partnership during his most recent meeting with his counterpart in the US.
He said Seoul was yet to make an application but "they have taken it onboard seriously".
"That's how close and friendly we are," he told a Senate hearing on Friday.
It comes at a tense time between Canberra and Beijing as the two nations work towards thawing trade disputes.
China is also pushing to join the CPTPP and wants Taiwan shut out of the pact.
Australia has maintained that the partner countries are working to deal with Britain's bid to join the grouping before turning to any other nation.
Senator Farrell has said any nation is welcome to apply and will be assessed on their merits and ability to adhere to strong trading principles.
Senator Farrell also rejected claims that Seoul was concerned about Australia's gas markets.
South Korean state-owned gas company Kogas has invested billions in Australia and raised concerns about gas export controls.
Japan's biggest oil and gas producer Inpex also raised concerns about government intervention in the gas market.
The trade minister said any Australian investment would need to comply with domestic laws, but added "the rules and regulations will be fair".
"Tell me another country that these countries can go to that have got the reliability, the certainty and the stability that Australia has got - there isn't one," he said.
He said all gas contracts would be honoured and would not impact other countries' transition to net-zero emissions and clean energy by using gas in the interim.
"You can't on one day turn off the gas and turn on the renewables - the real trick here is to ensure that investment remains," Senator Farrell said.
He said the government's policies and announcements had not impacted investment certainty and Australia's reliability as a gas supplier.
"They might make comments from time to time about some of our policies, but at the end of the day we are that safe, reliable, secure supplier and I don't think they can look elsewhere," he said.
"We will not get in a situation where we start breaking contracts."
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