The organisation, who are behind the Safe Standing campaign, claim that a host of clubs from the Premier League and Football League have backed the initiative, which they hope will bear fruit within "five to 10 years".
Scottish Premiership champions Celtic and the Scottish Professional Football League are also keen for standing areas to be introduced, the FSF said.
"We've come from a standing start two years ago when Aston Villa came on board and said, 'as a Premier League club, we would like to introduce safe standing areas'," Michael Brunskill of the FSF told Perform.
"Since then we've had dozens of clubs from the Premier League and the Football League who have formally backed the campaign.
"We've also had other clubs who are interested in it and press reports that Manchester City, Manchester United and West Ham are also interested.
"The Scottish Premier League as an institution has backed the safe standing campaign and they are in the process of doing what they need to do behind the scenes to ensure clubs can have safe standing areas.
"Celtic want a safe standing area at Celtic Park and also the Football League have voted overwhelmingly to explore the possibility.
"Once you start getting clubs as businesses and fans as consumers saying, 'yes we want this', I don't think there can be any argument."
With Manchester United the latest club reported to be interested in incorporating a standing section into their stadium, Brunskill hopes the involvement of the English champions will advance the FSF's objectives.
Asked if United's potential support would boost the push for safe standing, Brunskill said: "Absolutely.
"We want all clubs to come on board but if a club the size of Manchester United were to say they want it and tried to make it happen, then it's more likely to happen," he explained. "They're one of the biggest clubs in the world.
"In the past we've had politicians saying there is no demand for it, which we think is patently untrue, that would even more so be the case if Manchester United came on board.
"The reports are very encouraging and (United's) supporters certainly back safe standing when you read the polls and surveys that we've done but also when they go to away games, thousands and thousands of fans stand and the same goes for a lot of other clubs.
"It's absolutely the sensible option and I think we're moving in the right direction."
Many clubs in the Bundesliga have standing areas, as do stadia in the USA and Canada, but the practice has been banned in England's top two tiers after the Taylor Report into the Hillsborough tragedy in 1989.
Brunskill believes standing could return to England's higher levels within five years, something that would be helped by the likes of Manchester United backing the campaign.
On the subject of a time frame for the introduction of safe standing in the UK, Brunskill said: "That's the golden question.
"(I'd be surprised) if in the next five or 10 years you didn't see it. I think the next five to 10 years is a sensible range.
"If you did get Man United, and say that encouraged more Premier League clubs to get on board, that could speed up the process."
