The revelation could be made at the start of a new season.
Clarke said he hopes several players could come out at the same time so the focus would not be on one person.
The FA chairman also revealed he had held discussions with a number of top-level gay footballers, but stressed the final decision would always be left with the player.
“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, Football League and the FA could do it at the start of the season. At the start of the season, the crowds are happy, the sun is shining.”
Very few soccer players have come out during their active careers due mainly to the fear of a negative reaction from coaches, team mates and fans.
“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.”
Last year, Clarke said that he “wouldn’t recommend” a footballer coming out at the moment because of the risk they would be abused, but believes several players sharing the spotlight could be the answer.