Michael Forsyth, who took his officials by surprise when he expressed enthusiasm for the project at the previous Inverness meeting of MPs in February, could announce the lifting of the "cap" on higher education courses in the FE colleges that will form the core of the new university.
Robin Lingard, the university's project director, said: "There is a market for higher education work that is going unsatisfied. People do not go elsewhere for courses. They simply do not benefit at all."
Ray Murray, principal of Thurso College and chairman of the university's academic council, said: "There is a high level of expectation about what Mr Forsyth might say on structures."
Before the Highland colleges can evolve towards a university, the restriction on the volume of higher education work will have to be lifted. But if the cap imposed by the Scottish Office as part of the national curb on the expansion of higher education is removed only for the northern colleges, others would be loud in their complaints.
Graham Clark, principal of Falkirk College, said that he would be "very unhappy". There was considerable unmet demand for higher education in the Falkirk area, Dr Clark said, and students were unwilling to travel to Edinburgh, Glasgow or Stirling.
Falkirk has 1,000 higher-education students out of a total 2,000 full-time equivalents. Dr Clark believes that numbers could double if the cap is lifted.
Falkirk is a member of the Polytechnics Group, which includes Aberdeen, Fife, James Watt in Greenock and Telford in Edinburgh. Dr Clark thought that his fellow principals would share his views.
Mr Forsyth will answer a question from Margaret Ewing, SNP MP for Moray, during the Grand Committee meeting. He will take the opportunity to make a wider-ranging statement than her question demands. In February, reversing previous Government scepticism, Mr Forsyth said that his officials would explore fully the concept of a Highland university.
* The campaign for a University of Southern Scotland, based at the former Crichton Royal hospital in Dumfries but hopefully including the Scottish College of Textiles and Borders College, is to hold a public meeting on April 27.