The Demons' football department is based at AAMI Park, but the administration part of the business is located across a road and train tracks at the MCG.
News Ltd reported that Melbourne chiefs were in discussion with university management about the move, which would involve the redevelopment of the university's cricket ground.
Any move would still be some time away, but it fits with Demons president Glen Bartlett's plan to associate the club with the city of Melbourne.
The partnership could involve an off-field research section and help establish the Demons' brand at one of the world's most prestigious universities.
More to come