The FA plans to introduce what it calls "temporary dismissals" in England's step seven - six tiers below the National League - and the leagues below.
They will only apply to yellow cards shown for dissent, and will see players leave the field for 10 minutes.
It will also be tested in Sunday League and male and female youth football.
More than 1,000 clubs received emails over the weekend asking if they were willing to be part of the pilot process.
"There has already been a positive response with over 60 leagues in support of it," an FA spokesperson said.
Clubs are normally charged a £10 fine for each yellow card but the FA will not be charging this administration fee for those that participate.
Step seven is the bottom level of English football's National League System, which feeds into the country's professional leagues.
The highest league within that structure - step one - is the National League.
The move has been backed by teenage Sunday League referee Ryan Hampson, who earlier this year organised a nationwide strike by officials in protest at the amount of abuse they face in the grassroots game.
"There's obviously a lot more to be done but it's a step in the right direction and a great start," he told BBC Radio 5 live.
The Football Association will trial 'sin bins' in the lower leagues of English football from next season.