England’s FA had put forward the idea of sending Great Britain teams to the 2016 Olympics, but Fifa said it would need the agreement of all the ruling bodies.
Stewart Regan, the Scottish FA’s chief executive, was among those to voice concerns that a Great Britain team could impact the home nations at future international tournaments such as World Cups.
A spokesman for the Scottish FA told BBC Sport: “Our position remains that the Scottish FA does not support the playing of Olympic football under the Team GB banner, preferring all organised international football involving Scottish players to be played in the name of Scotland.”
In April, chief executive of the Football Association of Wales, Jonathan Ford, said he could now see the “merits” of a GB women’s football team.
In a statement to BBC Sport, the Irish Football Association said it “would not be in favour of sending players to a GB Olympic team. This is to protect our independent status within Fifa.”
England’s women, led by Mark Sampson, won a bronze medal at the 2015 World Cup and earlier this month reached the semi-finals of Euro 2017.
Glenn says the strength in depth through the nations could be key to further success.
“We would want to pick from the best of British talent and there’s a number from nations outside of England and we know that would be good for the game.”
Team GB entered men’s and women’s sides at London 2012, organised by the English FA.
Stuart Pearce took charge of the men and Hope Powell coached the women, with both teams being knocked out in the quarter-finals.