Justin Fashanu, who committed suicide in 1998, remains the only player to have come out while playing top-level football in England.
Homosexuality is seen as professional football's last taboo and Justin Fashanu, who committed suicide in 1998, remains the only player to have come out while playing top-level football in England.
Clarke said last year he "wouldn't recommend" a footballer coming out because of the risk they would face abuse, but he believes several players coming out at the same time could be a solution.
"I put the message out there that if a number of top-level pros want to come out, why don't we synchronise it? So one person doesn't have to come out on their own," he told The Times.
"The Premier League, the Football League and the FA could do it at the start of the season. At the start of the season everybody thinks it is their season, the crowds are happy, the sun is shining."
Clarke revealed he has spoken to gay sportspeople, including footballers, to discuss the best way forward.
"I've been asking the gay community, 'How can we provide more support and orchestrate it so that people get the right level of support if people want to be open about their sexuality?'" he said.
"I've met 15 gay sports people in the last four weeks to ask their views, including footballers.
"It is very difficult to get to a representative set of gay top-level footballers because some of them are happy with their sexuality and just don't want anyone to know.
"I don't want to be part of a process that says, 'You've got to come out.' That's not right. People are cautious. It's a one-way street. Once you're out of the closet, you're out."