The ex-footballer turned TV pundit, along with his brother Phil , Ryan Giggs and Paul Scholes, is in talks with Lancaster University to open a site in Greater Manchester.
It is understood that they are searching for possible locations in Stretford, Trafford. The university would offer courses including media, physiology and sports management, but specialise in sports studies.
The university project would include a degree of new build, although existing buildings could also be used as part of the development.
The uni could cater for as many as 5,000 students and include halls of residence.
A Lancaster University spokesman said: “We can confirm that we are discussing this project with Gary Neville, but we are still evaluating its feasibility and no decision has yet been made to proceed or otherwise.”