Employment and Learning Minister Stephen Farry says he will push for increased capacity at universities as hundreds of students scramble for places.
Demand continues to outstrip supply at Northern Ireland's universities.
In teaching colleges demand remains significantly higher than the number of places available – despite the dwindling number of jobs for qualified teachers here.
Stranmillis University College currently has 1,302 applicants – less than in 2012 and 2011 – for the 235 places available on its undergraduate courses.
At St Mary's University College, 951 people – slightly more than last year – are currently vying for 248 places.
At the University of Ulster, a total of 5,972 people have conditional and unconditional offers for one of the 5,000 undergraduate places.
Students with a conditional offer will have to get the required grades in their A-Levels results, released tomorrow. Students with unconditional offers are guaranteed a place.
At Queen's University, 5,500 people have a conditional or unconditional offer for one of the university's 4,036 undergraduate places. Another 1,500 local and EU students with insurance offers may also be competing for a place at the university when they receive their A-Level results.
Queen's University has said it will have around 100 places available through clearing, while the University of Ulster has yet to confirm how many it will offer.
The scramble for university places here has intensified since 2011 when tuition fees increased to £9,000 in Britain, but were frozen at £3,575 for local students going to university in Northern Ireland.
It means that students from Northern Ireland will face a bill of almost £11,000 at the end of a three-year course at local universities – compared to £27,000 if they study at a university in Britain. Students from England, Scotland and Wales are also competing for places at Northern Ireland's universities, where they will pay around £3,000 less a year in tuition fees than if they stayed at home.
Meanwhile, thousands of European students, keen to take advantage of Northern Ireland's cheaper fees, are also seeking the coveted places.
Mr Farry, the minister in charge of universities, is now facing calls to lift the limit on the number of places available here.
"We would call on the Minister for Employment and Learning to raise the MaSN (maximum student number) cap to undergraduates," Rebecca Hall, president of NUS-USI, said.
"The fact that there are only so many places available through clearing means potentially there are talented students in Northern Ireland who will have to look at options other than university."
However, North Antrim MLA Mervyn Storey noted the shortage of permanent teaching jobs available in Northern Ireland, and warned against creating more places on courses which will not offer immediate employment.
Mr Farry has said he is committed to expanding university places.
"I fully recognise the importance of a highly skilled and educated workforce to the economy of Northern Ireland.
"For that reason I am committed to the expansion of higher education and to making it accessible to as many people as possible," he said.
"Any expansion requires additional money and I have been able to secure the extra funding that has allowed me to increase the number of undergraduate places by 1,200 since I took up office," he added.
"I will continue to press for further growth and will bid for more resources as the opportunity arises."
Ucas revealed that 19,587 people had applied for places in Northern Ireland by the January 15 deadline. It is the highest ever number of applicants – an increase of 1,295 students compared to the same period last year.