Clarke believes there is a vocal minority who make it impossible for a leading player to come out as gay.
Football Association chairman Greg Clarke told members of parliament on Monday that he was ashamed of the sport's homophobia and admitted the governing body must do more to tackle the issue.
Clarke, who was speaking before the Culture, Media and Sport Committee, believes there is a vocal minority who make it impossible for a leading player to come out as gay.
The former Leicester chairman was in Westminster to answer questions about the FA's response to the corruption allegations reported by the Daily Telegraph last month but he was also asked if there were any gay players in the Premier League.
Clarke said he "would be amazed if we don't have gay players in the Premier League" and admitted that he was "ashamed players don't have the confidence to come out".
Clarke was also asked to explain why allegations made against Neil Warnock were not followed up during an MPs' hearing into football governance.
Allegations that Warnock was "crooked" and was "ruining the game" were made by Crystal Palace midfielder Jason Puncheon in 2014 on Twitter and quickly deleted.
They were repeated in Westminster by Damian Collins, the chairman-elect of the Culture, Media and Sport Committee, with Warnock responding that they were "completely and utterly false".
Clarke, who has only been FA chairman for five weeks, told Collins he did not know if the FA investigated Puncheon's claims about Warnock but suggested it certainly should have done so.
"I think it would be pretty poor if someone has gone public and they don't have any contact from the FA asking why have they made this allegation," Clarke said.