The called meeting is at 7 p.m. at the Woodstock City Hall Annex.
The Woodstock Downtown Development Authority, which is leading the pursuit, on Thursday night voted to draft a resolution for the cause and to sign an option to purchase a site.
The site location and its cost were not disclosed as the deal is pending, authority Executive Director Billy Peppers said.
The council at its meeting on Monday also will meet in closed session to talk about the purchase.
City officials have talked about locating the museum in either downtown or the Ridgewalk mixed-use development.
The deadline for the city to submit a formal request to the hall of fame's Authority is Friday.
Due to dwindling attendance and revenue, the state legislature gave the hall's authority the task of finding a new home for the museum.
Along with Woodstock, the cities of Dahlonega, Athens and Dunwoody are also lobbying to have the hall of fame relocate into their city limits.
The hall of fame authority has until April 15 to make a decision.