Welsh pair Giggs and Craig Bellamy are expected to join former England captain David Beckham in a star-studded GB line-up.
But Greene told the People: "I like football, in fact when I was a kid Giggs was my idol. I wanted to be like him down the left wing and I once had my picture taken with him.
"But the Olympics is not about football. These players do not grow up dreaming of an Olympic medal like the rest of us. They set their hearts on winning the Champions League or the World Cup.
"For me, an Olympic gold medal is all I've ever wanted.
"I think it is important that football does not take the focus away from other sports. Instead, this is the time in the next four years when people have the chance to get about badminton or table tennis.
"And, of course, the track are such an exciting part of the too. I have said before that football had no place at the Games, but I do hope they can do well.
"I just hope their success doesn't overshadow what everyone else achieves because this is all we have ever worked for as athletes.
"I don't get to represent Wales very often. I am usually running for Britain, so the Commonweal t h Games is about the only time I am just flying the flag for Wales. But when I am at the Olympics I want to do well for everyone back home.
"It is important to me because they give me such good support."