Universities are calling for the limit on tuition fees in England to be lifted so that they could rise with inflation above the current £9,000 maximum.
Universities UK, representing university leaders, says that the value of the fees, fixed since 2012, has been declining in real terms.
University heads want the value of tuition fees to be protected.
The Universities Minister, Jo Johnson, will tell university heads that they need to improve levels of teaching.
Mr Johnson is to give his first big speech as minister responsible for higher education, when he addresses a Universities UK meeting on Wednesday.
He will call for a much greater emphasis on improving the quality of teaching in universities, saying it should have equal status to ensuring the quality of research.
Living costs
But the university heads will call on the minister to increase funding for higher education.
They want the £9,000 cap on tuition fees to be lifted to increase funds for universities, and they want an increase in the maintenance support available to students.