Global governing bodies The Royal & Ancient and the US Golf Association have scheduled a teleconference amid speculation they will announce a ban on anchoring putters against the body, although any change isn't likely to take effect until 2016.
World No.5 Scott is highest-ranked player using a "broomstick", having done so with great effect over the past two years since switching.
The mood against them has gathered momentum since Bradley became the first player to win a major with a putter anchored on his midriff at last year's US PGA Championship. He was followed by Simpson at this year's US Open, and Ernie Els at the British Open.
Tiger Woods is opposed to long putters, and he stated his argument clearly on Tuesday.
"I just believe that the art of putting is swinging the club and controlling nerves, and having it as a fixed point - as I was saying all year - is something that's not in the traditions of the game," Woods said.
"We swing all other 13 clubs. The putter should be the same."
Woods said his biggest concern was not so much the major champions, but junior players.
"There have been some guys who had had success out there, and everyone always copies what we do out here, and that's something that, for the greater good of the game, needs to be adjusted."
Scott has already made his feelings about a possible ban well known, declaring the game has bigger issues with the way modern equipment is allowing golfers to overpower courses with long hitting.
He has also warned that the rule makers would have to be very careful to eliminate any uncertainties if they changed the rules.
"I've been successful putting with a short putter as well," Scott told Australian Golf Digest.
"They're not changing a rule concerning the length of the putter, it's more about whether it's anchored against the body. So I could still use the putter of the exact same length. It depends how they write the rule.
It's all speculation and for me it's not such a big issue as it is for some of the other guys who putt with belly putters, like Simpson and Keegan Bradley, who have never putted with anything else as a professional.
"It's not just about the professional game either, it's about the game in general and we don't want to be turning people away from the game because of the way they putt.
"If they're going to make a ruling, there can be no grey areas. But, like I said, I think they should get on with it and focus on what are the real priorities."
Simpson said on Tuesday he was ready to cope with whatever decision is handed down.
"I don't know what their definition of 'anchoring' is going to be," Simpson said, noting that US pro Matt Kuchar plays with a long putter that he holds against his forearm but which isn't anchored like a pendulum to his body.
"First of all, I think we've got to get a definition out," Simpson said.
"I'm not worried. I expected this day to come."
Bradley, who said in China earlier this month that he would do "whatever it takes to protect myself and the guys on tour," said on Tuesday that the assumption he meant legal action was premature at least.
"I never said the world 'sue'. I never said 'legal action'. Somehow it got twisted around into that," Bradley said.