The council-owned land, currently derelict, is located on Janefield Street and is used as a car park.
Glasgow City Council have owned the land since the 1940s, and Celtic are hopeful of securing ownership of the space to push ahead with the project, which has been in the works for some time.
If the authority sanctions the sale, any deal will reportedly include a sell-on clause.
• READ MORE - In pictures: The evolution of Celtic Park through the years
Fan zones are especially popular on the continent and with clubs south of the Border.
City Square, outside Manchester City’s Etihad Stadium, offers bar and cafe facilities as well as big screens and entertainment for fans ahead of kick-off.
A delegation from the Hoops attended a match between City and Aston Villa in 2014 with a view to gaining an insight into how City Square catered for fans.
• READ MORE - Celtic to set up match day fan zone