The University of Chester is negotiating with Lloyds Banking Group on the purchase of two offices totalling 65,000 sq ft in Queens Park Road, which would be converted into teaching facilities.
Cheshire West & Chester Council's planning committee approved the change of use of Capital House and Bridge House from offices to education buildings earlier this week.
The properties, which site on a six-acre site, were previously occupied by HBOS, a subsidiary of Lloyds, until the bank relocated in 2010.
Capital House was built in 1938 and remodelled in the late 1990s, while Bridge House was a part-replacement of a block demolished in the 1970s.
According to documents submitted to the planning committee, the buildings were brought to market in 2010 but out of 43 applicants only four house-builders put forward bids for the site which exceeded the guide price.
If the university secures the purchase of the site, it will relocate one of its eight faculties from the main campus on Parkgate Road to the site. There was no comment from the university as to which faculty would be moved.
Cassidy + Ashton advised the university on the change of use proposals.
Professor Tim Wheeler, the university's vice-chancellor, said: "Commercial sensitivities and legal constraints have restricted the university from announcing its interest in the property more publicly until we have reached this stage.
"We are optimistic of reaching a final agreement over the next few weeks, at which point we will be in a better position to be able to confirm more details.
"What we can say is that, subject to the sale going through, the iconic Capital House and Bridge House would provide teaching and associated facilities for one of our academic faculties and we can re-iterate that there are no plans for student accommodation."