No British team has competed in an Olympic finals since the introduction of women's football at the 1996 Atlanta Games, and there will be no British team at Beijing.
Keen fears the women's game will miss a huge opportunity if a team is not formed in the next four years.
Do we want that [vision] enough? I'd want it for my daughter - she loves football, what an image
Peter Keen
"In 2012 somebody is going to win the women's Olympic title in Wembley stadium," he said.
"Seeing a women's team representing Great Britain win in our national game, in our national stadium - to me, that's where you start this process from. What would it take to do that, and do we want that enough?
"I'd want it for my daughter - she loves football, what an image. How do we bring that about? I don't know, but a no-compromise winning mindset would find a way to do that, because it matters enough."
Keen is widely credited with inspiring the renaissance in British cycling, where he previously acted as performance director.
He is now responsible for delivering British success at London 2012, but the creation of a British women's football team depends on the Football Associations of England, Scotland, Wales and Northern Ireland.
In October 2007, the chief of the British Olympic Association, Simon Clegg, told the BBC's Inside Sport programme he was determined to field both men's and women's teams for 2012.
But opposition to the move has been strong, with the Welsh, Scottish and Irish associations putting up resistance.
"We would not want to compromise our national identity," Irish Football Association president Raymond Kennedy told BBC Sport last year.
Keen says the responsibility for overcoming that hurdle and creating a British team lies with the game.
"You'd have to have football find a way to make it work.
"The expertise is in this country - we're the fifth or sixth best nation in the world now. We should be winning that [gold in 2012].
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