"Do I think we should have a team representing football in the 2012 Olympics? Yes," Barwick said. "We have to respect the views of Scotland, Wales and Northern Ireland, but this is an Olympics that is going to take place in London in four years time. There's an appetite for us to have a team," he added.
The Scottish, Welsh and Northern Ireland FA's are opposed to the idea as they argue that their voting rights within Fifa would be undermined should they agree to compete under the Great Britain banner.
The FA chairman Lord David Triesman is similarly enthusiastic, saying it would be "barking mad" if Britain did not field a football team at the London Olympics.
"I can see no good reason for not having one at all. Whatever it has to be comprised of, we will have a team in the 2012 Olympics," Triesman said.