The Football Association plans to enter men's and women's Great Britain teams for the 2016 Olympics.
It had ruled out such a move but has now written to its counterparts in Scotland, Northern Ireland and Wales to ask them if they want to take part.
A British Olympic Association official revealed it had "received confirmation" of the FA's plan for Rio de Janeiro.
Both GB teams would have to qualify and football's world governing body Fifa would also have to sanction the move.
The results of the England men's and women's teams are taken into account when it comes to Team GB qualification as the English FA is the national governing body on the BOA.
Therefore, England would need to finish in the top four at the European Under-21 Championship for the men to qualify.
For the women, England would need to be one of the top three European teams at the World Cup in Canada.
Both tournaments take place this summer.
Several players from the home nations featured for GB at the London 2012 Games despite Scotland, Wales and Northern Ireland refusing to give their official backing.
Five Welsh players, including Ryan Giggs and Aaron Ramsey, were named in the men's squad, while Scottish duo Ifeoma Dieke and Kim Little made the women's squad.
|GB men's squad for 2012 Olympics|
|Goalkeepers: Jack Butland, Jason Steele (both England).|
|Defenders: Neil Taylor (Wales), Ryan Bertrand, Steven Caulker, Craig Dawson, James Tomkins, Micah Richards, Danny Rose (all England).|
|Midfielders: Aaron Ramsey, Joe Allen, Ryan Giggs (all Wales), Tom Cleverley, Jack Cork (both England).|
|Forwards: Scott Sinclair, Daniel Sturridge, Marvin Sordell (all England), Craig Bellamy (Wales).|
Northern Ireland, Scotland and Wales were afraid a Great Britain squad could set a precedent that affected their individual status.
On the latest development, an FA of Wales spokesman told BBC Sport: "We are making no official comment at the moment."
The Scottish FA's stance is believed to be unchanged from London 2012 when they opposed a Team GB but did not prevent its players from taking part.
Its opposition is based on the threat that backing a Team GB could poses a risk to its individual memberships of Fifa and the International Football Association Board.
IFAB consists of four British associations and four from world governing body Fifa and is football's ultimate rule-making body.
The Irish FA issued the following statement: "The Irish FA has not changed its position from before. The association was of the understanding that participation at the London Olympics was a one off.
"The Irish FA believes that, when playing, our players should play in a Northern Ireland shirt."
The GB men's side, coached by Stuart Pearce, lost on penalties to South Korea in the quarter-finals in 2012.
|GB women's squad for 2012 Olympics|
|Goalkeepers: Karen Bardsley, Rachel Brown (both England).|
|Defenders: Alex Scott, Steph Houghton, Sophie Bradley, Casey Stoney, Claire Rafferty, Dunia Susi (all England), Ifeoma Dieke (Scotland).|
|Midfielders: Jill Scott, Fara Williams, Anita Asante (all England), Kim Little (Scotland).|
|Forwards: Karen Carney, Ellen White, Kelly Smith, Rachel Yankey, Eniola Aluko, Rachel Williams (all England).|
The women's team also lost at the quarter-final stage, to Canada, but not before a crowd of 70,584 - a record for a women's game in Britain - saw GB beat group rivals Brazil 1-0 at Wembley.