He says it would stop terrace slurs from opposing supporters.
The FA chairman said he hoped the association, Premier and Football League could help “sychronise” a mass outing at the start of the season when the crowds are happy and the “sun is shining”.
He spoke out after meeting 15 top gay sports personalities – including footballers.
“I put the message out there that if a number of top-level pros want to come out why don’t we synchronise it?”
Mr Clarke said: “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. I was asked if football is ready for top-level pros to come out and I said I’m not sure we were.
“There was a survey which said people would support gay people in their own team, yes.
“But I’m worried about what they said about gay people in the other team, not that they would do bad things, but I said we should prepare well.
“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.’”
Only four UK-based players have ever openly admitted they are gay.
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