Great Britain could again take part in the football tournament at the next Olympic Games in 2020, according to British Olympic Association chief executive Bill Sweeney.
Britain made an exception when entering men's and women's teams for the 2012 Olympics in London after having ceased to compete in the tournament after 1974, when rules were changed to allow professionals to take part.
Despite the English FA having been keen to see Team GB represented in the football tournament at the Rio Olympics this summer, the Scottish, Welsh and Northern Irish FAs failed to give consent amid longstanding concerns that doing so could jeopardise their status as independent nations within the sport.
Despite Britain's great overall success at the Rio Olympics, Sweeney expressed disappointment that no football team had taken part and said talks would take place to try to field teams in Tokyo in four years' time.
"We are all desperately disappointed that there isn't a football team for Team GB, primarily the women's because they are so strong, had a great season leading up to this, but also on the men's side as well," Sweeney told reporters.
"We'll be having meetings when we get back to try and sort that out with the FA. If you look at the success of women's hockey here, to have had a similar sort of story in football would have been absolutely fantastic.
"I think the athletes would have loved the environment and would have loved to have had the chance to perform at their best in a country like Brazil, which is so passionate about football."
British Olympic Association vice-chairman and former sports minister Sir Hugh Robertson told BBC 5 live's Sportsweek: "From the British Olympic Committee's perspective, we would love to see Team GB football. It is particularly a powerful tool to promote the women's game.
"The tragedy is that the politics of football administrators impact on the athletes because women football players would want to be at the Olympics."
New England manager Sam Allardyce added on Sportsweek: "To turn it down is a great shame. It's something we may look at in the future and try to compete in."
The men's team at the 2012 Olympics was coached by Stuart Pearce and featured players including Ryan Giggs, Daniel Sturridge, Aaron Ramsey and Craig Bellamy, reaching the quarterfinal stage.
Hope Powell's women's side won three games out of three in the group stage but was also eliminated after reaching the quarterfinals.