The FSF will hold a series of meetings across the country aimed at finding ways of reducing costs, particularly for away fans. It comes after Manchester City returned 912 unsold tickets priced at £62 each to Arsenal ahead of this weekend's match at the Emirates.
The Premier League are also looking into ways of boosting the number of away fans, such as by subsidising coach travel.
Stoke have suggested to a league working group that coach travel could even be provided free and paid for by a central fund, and that away tickets are never more expensive than the cheapest home ticket.
An FSF statement said: "Match-going fans all too often must pay through the nose to watch their team.
"The problem is particularly acute for away fans who must also cover the additional costs of transport, food and refreshment that come with following your team across the country.
"Reports suggest that the Premier League is exploring the idea of an away fans' fund - this sounds like a welcome initiative and one of many potential options that we would be pleased to explore with them.
"Of course high prices affect supporters in all leagues, and solutions must be found for those fans too. In the last few days there have been many petitions and local campaigns aiming to bring away ticket prices down to a more affordable level.
"This feels like a real watershed moment when fans across the country are willing to put aside club differences to speak with one voice. With that in mind the Football Supporters' Federation will next week announce the first in a series of meetings across the country to see what fans can do to make football more affordable."
One petition, started on campaign website Change.org by Manchester City fan Richard Hincks, has been signed by more than 2,000 fans.