Around 150,000 of those school places are expected to come from the private sector, auditing firm PwC said in its report entitled "GCC Education Sector: a country by country overview".
According to the report, the number of private schools in the kingdom has grown at a rate of 3 percent per year.
The strongest growth has been in primary education, while
where enrolment in public schools has fallen.
While a 25 percent growth in market share of would be welcomed, private schools are unlikely to reach beyond 11 percent unless drastic changes are made, the report said.
"With an already high university enrolment rate - predominantly at public institutions - the kingdom is facing budgetary pressure and a shortage of good alternatives to public universities," said Sally Jeffery from PwC, a professional services firm.
"In the coming years, it will be crucial for the government to help deliver more private sector education provision."
PwC also said that tightening visa restrictions and more stringent scholarship requirements may cause a significant portion of the 190,000 Saudi students who study abroad each year to seek further education at home.
The pressure that this could put on higher education places may mean a greater demand for private institutions.
Saudi Arabia is currently undergoing a series of economic reforms in order to wean its oil-dependant economy away from its most prized commodity.
This programme of reform has included austerity measures that have cut public funding and subsidies.
If the kingdom experiences continued high enrolment rates - while the country's university age population also continues to grow - around 125,000 more places will be needed in post-secondary education by 2020.
The projections made by the auditing firm raise questions about what kind of alternatives that can be offered to university education, particularly as the country wishes to move to a knowledge-based economy.