The Football Association wants a Great Britain women's football team to be revived for the 2020 Olympics in Tokyo.
GB teams played at the 2012 Games in London but will not feature in Rio.
The FA wanted to see a joint side take part this summer too, until its Northern Irish, Scottish and Welsh counterparts objected.
But FA participation and development director Kelly Simmons said: "The door's definitely open from our side to continue discussions."
A change at the top of Fifa, with Gianni Infantino replacing Sepp Blatter as president, has given the FA fresh hope that the home nations could be reassured about their status as stand-alone footballing countries if they support a GB team.
At Wednesday's launch of the Women's Super League season, Simmons stressed the importance of the Olympics for the development of the women's game.
And she rued the lack of a joint women's team in Brazil, to build on the success of England's World Cup performance last summer: "It's a massive blow. Here we are still working hard to promote the game, build a new fan base and take it to new audiences, and those big events are really critical in that."
The other home nations object on the basis that London was a one-off as hosts, and they fear a united British team could risk their independence as football nations within the sport's world governing body, Fifa.
"I hope that somehow we can find a way with the home nations and Fifa in the future, if we qualify, to take part, because the players deserve it and the women's game needs it," Simmons added.
A crowd of 70,584 watched Great Britain's women beat fancied Brazil 1-0 to reach the quarter-finals in 2012.
Simmons' comments echo those of British Olympic chiefs who said they would campaign to restore a GB side for 2020 following a third-place finish at last year's World Cup for England's women.