If Kmart wins the case, it will be allowed to continue occupying the space under its lease with Harvard. The lease expired last February and was planned to be extended until January 2009.

Many Harvard and Kmart officials declined to comment on the issue because of the pending litigation.

The Allston Kmart is situated across the Charles River from Harvard Yard, beyond the Harvard Business School. Target, a competing discount retail store, is located nearby in Watertown.

The dispute comes as Harvard continues to develop its plans for expanding the campus into Allston.

“There are no plans for building anything there at this time,” Wrinn said. “This is an ongoing and isolated issue, not related to any specific plans for use of that property.”

“Any proposals for development of any Allston property would include extensive consultation with our Allston neighbors and the City of Boston,” he added.

According to Wrinn, Harvard has not asked Shaw’s or any other businesses in the Brighton Mills Shopping Center to leave.