Allowing wealthy families to "leapfrog" the system by playing for places is not the answer to the challenges the sector is facing, a union leader has said.
Sir Peter Mathieson, Principal and Vice-Chancellor of the University of Edinburgh, said the idea was "worthy of calm consideration" to keep money in the Scottish system and prevent a talent exodus.
In 2022, Edinburgh received 75,438 applications for around 6000 places, an increase of more than 17,000 compared to 2018.
The Scottish Government caps the number of Scottish students each university can take while institutions are also bound by 'widening participation' quotas.
Mary Senior, Scotland official of the University and College Union (UCU) said a two-tier system that "marketised and commodified" education was not something to aspire to.