Most sports fans in England, Wales and Scotland say they would be comfortable with their club signing a gay player, according to a BBC Radio 5 live survey.
It found 82% of supporters would have no issue with a gay player.
However, 8% of football fans said they would stop watching their team.
Last week, Football Association chairman Greg Clarke told MPs he was "cautious" of encouraging a player to come out because they may suffer "significant abuse" from fans.
Speaking to BBC Radio 5 live on Wednesday, Clarke said he stood by his "personal view" that "vile abuse" from a "small minority on the terraces" must be solved before any gay footballers "take that risk" to come out.
"If they want to take that risk I would respect them and support them," said Clarke. "But we can't promise to provide them at the moment with the required protection. We need to redouble our efforts to provide that safe space."
Clarke added that he hoped to achieve that in a "year or two".
In an online survey of more than 4,000 people commissioned by Afternoon Edition and carried out by ComRes, 71% of football fans said clubs should do more to educate fans about homophobia.
And 47% of all sports fans - 50% of football supporters - say they have heard homophobic abuse at matches.
Former Premier League striker Chris Sutton told Afternoon Edition that Clarke had "taken the easy way out" by being "dictated to by 8% of cavemen".
Sutton, who played for Norwich, Blackburn, Chelsea and Celtic, said: "Coming out wouldn't be a problem in the workplace. Working at a football club is just like anywhere else. Players I played with wouldn't bat an eyelid.
"This 8% shouldn't be allowed in football grounds. By not taking it on, the 8% are the winners in all of this. Greg Clarke should be taking these people on.
"It's bonkers in our society that people like this can dictate whether someone can come out or not."
The survey of fans of 11 different sports also found:
More sports fans (12%) would feel uncomfortable with a rival player joining their club than a gay player (8%)
7% of sports fans would stop watching their team if they signed a gay player
57% of sports fans believe gay players should come out to help others do the same
18% of sports fans believe gay players should "keep it to themselves"
15% of sports fans think having a gay player on a team would make other team-mates feel uncomfortable
50% of football fans say they have heard homophobic abuse, 51% have heard sexist abuse and 59% have heard racist abuse.
http://www.bbc.co.uk/sport/37760114
Sigh
It found 82% of supporters would have no issue with a gay player.
However, 8% of football fans said they would stop watching their team.
Last week, Football Association chairman Greg Clarke told MPs he was "cautious" of encouraging a player to come out because they may suffer "significant abuse" from fans.
Speaking to BBC Radio 5 live on Wednesday, Clarke said he stood by his "personal view" that "vile abuse" from a "small minority on the terraces" must be solved before any gay footballers "take that risk" to come out.
"If they want to take that risk I would respect them and support them," said Clarke. "But we can't promise to provide them at the moment with the required protection. We need to redouble our efforts to provide that safe space."
Clarke added that he hoped to achieve that in a "year or two".
In an online survey of more than 4,000 people commissioned by Afternoon Edition and carried out by ComRes, 71% of football fans said clubs should do more to educate fans about homophobia.
And 47% of all sports fans - 50% of football supporters - say they have heard homophobic abuse at matches.
Former Premier League striker Chris Sutton told Afternoon Edition that Clarke had "taken the easy way out" by being "dictated to by 8% of cavemen".
Sutton, who played for Norwich, Blackburn, Chelsea and Celtic, said: "Coming out wouldn't be a problem in the workplace. Working at a football club is just like anywhere else. Players I played with wouldn't bat an eyelid.
"This 8% shouldn't be allowed in football grounds. By not taking it on, the 8% are the winners in all of this. Greg Clarke should be taking these people on.
"It's bonkers in our society that people like this can dictate whether someone can come out or not."
The survey of fans of 11 different sports also found:
More sports fans (12%) would feel uncomfortable with a rival player joining their club than a gay player (8%)
7% of sports fans would stop watching their team if they signed a gay player
57% of sports fans believe gay players should come out to help others do the same
18% of sports fans believe gay players should "keep it to themselves"
15% of sports fans think having a gay player on a team would make other team-mates feel uncomfortable
50% of football fans say they have heard homophobic abuse, 51% have heard sexist abuse and 59% have heard racist abuse.
http://www.bbc.co.uk/sport/37760114
Sigh