The one-time Junior Food Store has been closed for many years and is in need of repairs.
In the 1990's it was donated to the city. A local church showed interest in converting the building into a thrift shop.
A second group would like to transform it into a teen club.
Councilwoman Vicky Harrison says she would like to study all options before making any kind of decision.
The New Brockton council plans to take up the issue of the old convenience store in coming weeks during a workshop session.