Stuart Pearce wants the Scottish, Northern Irish and Welsh Football Associations to make their players available for the London 2012 Olympics.
Hope Powell has been appointed to take charge of Great Britain's women's side, while Pearce will manage the men's.
And Pearce said: "I'm not going into this job looking only to select English players. If at all possible, it should be made up of all the home nations.
"They should come forward and put their players up for selection."
The Wales and Scottish football association have reiterated their opposition to a British team as they feel it threatens their independence as football nations.
It is understood the Northern Ireland FA also remains opposed.
Despite assurances from Fifa, the nations are concerned that selection of their players will undermine their independent status in the international game.
The 18-strong men's squads must contain 15 players who were born on, or after, 1 January 1989 - but three players can be older. There are no age limits for the women's selections.
But Pearce, the England Under-21 manager since 2007, added: "A lot of it will depend on the players' mentality. If the players want to be part of it, that would be fantastic. I think they will.
"I think they will be very, very excited to be part of this showcase of football.
"Dialogue will come into it between myself, the federations, and the managers concerned. I think support will be galvanised as the months go by and the tournament nears kick-off."
But former Scotland manager Craig Brown doesn't want Scottish players to play.
He told BBC Radio 5 live: "I wish them every success but I would still be disappointed if any selected Scottish player took part.
"We fear the autonomy of Scottish football would be jeopardised if we were to play and it would be selfish of the player."
Despite the position of their FA, Welsh youngsters - Tottenham's Gareth Bale, 22, and Arsenal's Aaron Ramsey, 20 - have already stated their willingness to be a part of the squad.
Former England captain David Beckham, 36, is also known to be keen to represent Great Britain.
Pearce said he would only select players on "form and fitness" - and refused to be drawn on whether Beckham will be included.
"I've not seen him play recently, he's a bit old for the Under-21s," Pearce joked.
"I was fortunate to be part of Euro 96, so I know how special it can be to play for your country on home soil at a major tournament.
"I'm sure this group of players will relish being part of not only a huge tournament in this country, but a unique one competing together and representing the UK."
Powell has led England's women for 13 years, including four successive major finals, including Euro 2005 on home soil.
She said: "The attendances at the games during Euro 2005 were a sign of progress for women's football in this country. It helped provide a platform for what has happened since then.
"I'm delighted to be in the position to be able to take a team into such an illustrious tournament, I just wish it were starting tomorrow."
The Football Association made the appointments after being instructed by the British Olympic Association to oversee Team GB.
FA chairman David Bernstein said: "With their excellent track record and experience I am convinced we have chosen the best coaches for these positions."
Britain will field a men's team for the first time since the Rome Games of 1960, while the women are making their debut.
But a Scottish FA spokesperson said supporters agreed with their stance.
"We have been consistently clear in our position and, in particular, the threat it poses to our independent membership of FIFA and also our representation on the International Football Association Board," the spokesman said.
"It is imperative we preserve our voice at the top table of world football and the supporters are in agreement with our stance.
"We have consulted with the men's and women's international squads in order that they understand our position, the reasons for that position and are aware of the feelings of the supporters."