Team GB's women squad, including two Scots and no players from Wales and Northern Ireland, reached the quarter-finals at London 2012.
The Welsh, Scottish and Northern Irish associations refused to keep the combined team going for Rio 2016.
But Clarke wants "a partnership of equals" to reform a joint women's team.
He added: "The home nations are discussing how we can achieve that for the women's game.
"We've got a follow-up meeting to look at the practicalities of making it happen.
"I'm hopeful that the four of us together (England, Scotland, Wales, Northern Ireland) will create a partnership of equals that will allow our women to compete in the Olympics going forward."
Clarke did not address any possibility of a men's GB team also being rekindled after appearing at the 2012 Games and not doing so four years later.
Football Association of Wales (FAW) chief executive Jonathan Ford confirmed in September 2016 that the home nations had met informally to discuss Team GB teams at future Olympics.
Ford also stated at that time there had been no change to the FAW's stance over men's and women's teams on the issue.
Wales, Scotland and Northern Ireland are thought to fear such a move could affect their independent status within Fifa and at international tournaments such as the World Cup.
Football Association chairman Greg Clarke remains hopeful a women's team will represent Great Britain at future Olympic Games.