England manager Sam Allardyce would welcome Team GB competing in football at future Olympics.
Despite taking part in London 2012, the four national football associations were unable to agree on sending Great Britain teams to the Rio Games.
Allardyce told BBC 5 live’s Sportsweek: “It is a fantastic venue once every four years and to turn it down is a great shame.
“It’s something we may look at in the future and try to compete in.”
Allardyce, who replaced Roy Hodgson after Euro 2016, added: “When you see the delight on Justin Rose’s face after winning the gold medal in golf it shows what it all means.”
England’s Football Association had put forward the idea of sending Great Britain teams to the Olympics, but Fifa said it would need the agreement of the ruling bodies in Scotland, Wales and Northern Ireland, who were against it.
The other home nations fear such a move could affect their independent status within the sport’s world governing body Fifa and at international tournaments such as the World Cup.
Team GB entered men’s and women’s sides at London 2012, with Stuart Pearce coaching the men and Hope Powell the women. Both teams were knocked out in the quarter-finals.
Olympics would boost women’s game
British Olympic Association vice-chairman and former sports minister Sir Hugh Robertson believes politics in particular has denied the women’s game a perfect platform to build on the interest it received at London 2012.
A total of 154,998 people turned out to watch the four Team GB women’s matches four years ago.
“From the British Olympic Committee’s perspective, we would love to see Team GB football,” Robertson told Sportsweek.
“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.”