FA chairman Greg Clarke says he is "personally ashamed" that gay football players do not feel safe to come out.
Facing questions from the Culture, Media and Sport select committee of MPs, Clarke insisted the environment of football could not guarantee gay players would not receive abuse from supporters.
Clarke admitted he is aware of at least two gay players in the Premier League, one of them an England international, who had expressed a desire to come out last season, but never did.
On the same day an investigation was launched into allegations of Luton supporters shouting homophobic abuse at Leyton Orient, Clarke said he is determined to stamp this "abhorrent" behaviour out of the game.
"I would be amazed if we haven't got gay players in the Premier League and I am personally ashamed they don't feel safe to come out," Clarke said.
"I think what we have in football is a cross-section of society. When you get a sample size of four million - 10 per cent of the population - they tend to trend towards mainstream society. But there is a very, very small minority who hurl vile abuse at people they perceive to be different.
"There was an example at the weekend. There were allegations at Leyton Orient versus Luton, that the Luton fans were hurling homophobic abuse at a group of men they perceived to be gay. That behaviour is disgusting and I am absolutely determined we stamp it out.
"Our job is to identify anybody guilty of persecuting, in any way, members of an ethnic or gender minority - because women get abuse too - and come down like a tonne of bricks and make sure these kinds of abhorrent behaviour are driven out."
Justin Fashanu was the first openly gay footballer, coming out in 1990, but he was subjected to a torrent of abuse from fellow players and supporters, leading to his eventual suicide in 1998.
Former Aston Villa player Thomas Hitzlsperger waited until his retirement to disclose he was gay, while former USA international Robbie Rogers came out in 2013 after leaving Leeds United.
Clarke said: "One of the questions we have is; if you have a son who is gay and plays top level football, would you encourage him to come out with the expectation of abuse he is going to get?
"I watched David Beckham get vile abuse for dating a pop star years ago, and it made me sick to my stomach. If it was a gay man, why would I expose myself to that? If a player came out now there would be significant abuse because I don't think we have cracked the problem yet.
"I know what it is [the reason they don't come out]. Before we encourage people to do that we must create the safe space where they can expect to be respected, and not be abused."