The sports facility would have a standard pitch and training facilities in Auchinairn, East Dunbartonshire.
According to BBC Sport, it would be used by the Glasgow City Foundation and other community groups.
Glasgow City Foundation's Douglas Barnett said: "This will be the first purpose-built women's football facility in the UK - promoting the sport to new generations of girls and women."
The foundation, the charitable element of Glasgow City Football Club, and East Dumbartonshire Council are entering into a formal agreement to explore the development of a joint sport and community well-being facility.
City have played the majority of their home games in recent years at Springburn's Petershill Park and Airdrie's Excelsior Stadium.
Council leader Rhondda Geekie said: "This agreement follows recent engagement with the local community to determine whether there was interest in working with Glasgow City Foundation to explore the potential for a sporting facility alongside our place approach and the new community facilities we are planning for this area.
"Through both the information session we held in May and the online survey we hosted on the council website, there was overwhelming support for the development of this proposal from those who took part."
City have won the Scottish title eight times in a row and made it as far as the quarter-finals of last season's Champions League.
Last week, head coach Eddie Wolecki Black announced he was stepping down after eight years at the club.