The chief of the Indonesian Investment Coordinating Board, Thomas Lembong, revealed negotiations on the deal - known as the Comprehensive Economic Partnership Agreement - were "70 per cent completed".

However he said Australia wanted the education sector included in the deal, given Australia was already the number one destination for Indonesian students studying abroad and other countries, such as Malaysia, allowed foreign universities.

"So they are asking if Australian universities can operate in Indonesia. This is a breakthrough they [negotiators] are still working on," Mr Lembong said.

Finalising the free trade agreement will be one of the key topics of discussion when Indonesian President Joko Widodo flies to Australia this weekend to meet with Prime Minister Malcolm Turnbull.

Fairfax Media understands RMIT - which already has a successful campus in Vietnam - has made several exploratory trips to Indonesia.

RMIT University's deputy vice-chancellor of global development, professor Andrew Macintyre, said the university had no current plans to open a campus in Indonesia. But he said he strongly supported including education in the trade deal.

"It will lead to a broadening and a deepening of Australia engagement with Indonesia in higher education," he said. He said the two countries had a lot to offer each other.

"Indonesia is a really important country for us," he said. "Our approach is focused on working with our partners there rather than seeking to establish our own campus there."

Swinburne deputy vice-chancellor professor Duncan Bentley said the university considered Indonesia a "key" long-term partner.

The Victorian university already has a campus in Malaysia where students from more than 60 countries study.

Professor Bentley said this campus, which is located on the island of Borneo, had enabled the university to strengthen its ties with Indonesia through research and education.

"Swinburne encourages students and staff to engage with our South-east Asian neighbours, including Indonesia, through research partnerships, education partnerships, student exchange and industry study tours," he said.

A number of smaller universities and TAFEs have also expressed interest.

However the Australian Department of Education and Training said that unlike in Singapore and Malaysia, "no Australian higher education provider is able to operate a stand-alone campus in Indonesia".

Fairfax Media understands this is for a range of reasons, including concerns about competition for students from local universities and regulations that severely inhibit foreign investment in education and training in Indonesia.

"Despite the length and depth of our bilateral education relationship, the great demand for educating and training in Indonesia and genuine potential for mutual benefit, barriers remain to expanding Australian education exports to Indonesia," the department said in a submission to a current parliamentary inquiry into Australia's trade and investment relationship with Indonesia.

The department supported a trade deal that "could open new market access and reduce behind-the-border barriers for Australian education and training providers so that they can help meet Indonesia's need for a skilled and educated workforce".

TAFE Directors Australia chief executive Martin Reardon said the proposed changes would benefit Australian TAFEs.

He said a recent survey conducted by the organisation and Austrade identified "quite alarming" skills shortages in Indonesia, particularly in the services industry and construction.

"We feel quite prepared," he said. "It's a win-win scenario."

In China, Australian TAFEs have forged around 90 partnerships with local institutions.

This has led to 45,000 Chinese students undertaking Australian diploma courses every year.

"They have no interest to come to Australia but just want to get a better job in China," he said.

"The Indonesian ministry of education has been very keen for us to look at similar programs for Indonesian students to do technical qualifications in English and maybe even special academies."

The International Education Association of Australia says there are only about 19,000 Indonesian students currently studying in Australia.

"The irony is Australia is still the most popular study destination for Indonesian students," said executive director Phil Honeywood.

"There's still a massive potential market if we could provide the benefits of an Australian education in Indonesia," he said. "There is an incredible appetite on behalf of all Australian education providers to enhance delivery into Indonesia."

The Australia Indonesia Business Council is also pushing for the trade deal to include provisions to open the university sector in Indonesia to foreign investment.

"Despite the criticality of skills for both nations, and the high potential for both to benefit, cooperation in education and training has been fitful," it said in a submission to the inquiry.

Council president Debnath Guharoy told Fairfax Media that any major economy should have at least 10 per cent of its workforce university or tertiary-educated.

"Indonesia stands at four per cent," he said. "Everybody understands Australia can make a major contribution to economic uplift in Indonesia if the gates are more open."

Mr Lembong, a former trade minister, has previously hinted that Indonesia could allow Australian campuses in special economic zones.

This week he said Indonesia considered negotiations on the trade deal had been "very conducive" and they remained confident it could be wrapped up this year.

"If we wanted to we could finalise it today," he said. However he said this would be a waste as it was hoped the agreement would be as wide as possible.

"This is such a rare opportunity. So we want it to be as ambitious as possible in terms of the coverage of the agreement."

Australian Trade Minister Steve Ciobo said there was significant scope in the free trade agreement to build the services relationship between Indonesia and Australia in a number of areas. These included education, financial, professional and mining services.

"Likewise we can secure new opportunities for Australian goods into Indonesia," Mr Ciobo told Fairfax Media.

"The Indonesia Australia Comprehensive Economic Partnership Agreement is an historic opportunity to redefine the bilateral economic relationship, by increasing the flow of goods and services and raising  levels of investment to new levels," he said.

"Australian and Indonesian negotiators are working towards a timely conclusion of a quality free trade agreement with Indonesia and have made good progress in talks this week in Canberra. Both sides are committed to delivering a high-quality deal this year."

Despite the geographical proximity between the two countries and the burgeoning middle class in Indonesia, the adjective most frequently used to describe the trade and investment relationship is "underdone".

Indonesia is Australia's 12th-largest trading partner and there are only about 250 Australian businesses in Indonesia.