Speaking on 29 May at the Gulf Education Conference in London, David Willetts said that higher education, which was already a “great British export industry”, could be “far bigger”.
He said that he wanted to see an expansion because “growth is the government’s agenda, and we want to see it grow”.
“Our well-regarded, well-run and properly audited universities are one of our great assets, and we’re going to expect more of them in terms of overseas students,” he said.
Mr Willetts is preparing a major speech to be delivered at Stanford University later this month, where “international investors who want to fund that expansion” will be listening, he said.
The context of a tougher visa regime for students entering the UK means Mr Willetts may envisage British universities expanding their provision for international students overseas, through branch campuses or other forms of transnational education.
Home Office ministers have spoken about cutting the overall number of international students coming to the UK.
In March 2011, Theresa May, the home secretary, promised to cut the number of students entering the UK by 80,000 a year by setting tougher entrance requirements, not least on English-language abilities.
Last month, data from the Office for National Statistics showed that net migration totalled 252,000, still close to record levels, in the year to September 2011. Students made up the largest group of immigrants.
The government has pledged to reduce net migration to below 100,000 by 2015.
Universities UK has called for student immigrants to be excluded from the official count unless they decide to settle in the UK more permanently.
At the conference, Mr Willetts said that the UK sector had a “lot to offer” universities in the Gulf.
“We are very keen to foster genuine partnership, student exchange, system-to-system exchanges of ideas,” he said.
The UK could share advice on areas including accreditation, quality assurance, building design, and curriculum design, he said.