The move comes days after Rutgers University defensive tackle Eric LeGrand was left paralyzed from the neck down during a college game and several NFL players suffered head injuries.
Doctors fear LeGrand's spinal cord injury may be permanent.
"It's like he hit just wrong," Rutgers coach Greg Schiano said. "I really had a bad feeling, and when I got out there, it was exactly what I feared."
"If we talk about someone who has a completed spinal cord injury that does not improve in 72 hours that person won't recover," said Dr. Roy Vingan of the Hackensack University Medical Center where LeGrand is being treated.
On the pro teams, several players suffered possible concussions this weekend after deliberate helmet-to-helmet hits.
"These concussions as I saw it were head-to-head contact," Dr. Julian Bailes, chairman of neurosurgery at West Virginia University told "Good Morning America" today. "Deliberately targeting the other players head and that's really, really troubling that that's continuing."
The NFL's Ray Anderson called violent play like that "egregious" and "flagrant," in an interview with The Associated Press. Officials have promised to be more aggressive in penalizing players.
"Going forward there are certain hits that occurred that will be more susceptible to suspension," Anderson said.
Twelve players have already been fined this kind of play this year.
ESPN reported that an official announcement could come as early as Wednesday. The new policy could then go into effect for this weekend's games, "Good Morning America" contributor Erin Andrews said.
But in a sport where the hard plays are rewarded with instant replays and fan enthusiasm, it may take more than just a crackdown.
"It has to be a culture change. Everyone has to buy in," Bailes said. "It has to start from the top down at the NFL level."
"I think this is a good plan if it comes to fruition this week," he said.
ESPN's Merrill Hodge, whose own career was cut short because of repeated concussions, applauded the NFL.
"Your helmet is used for protection. It is not a weapon," he said. "When you see it's deliberate, we need to suspend those guys and penalize them."
But, Andrews noted, some football officials don't see the sport as dangerous.
"I spoke with a few college coaches last night and I asked them, 'Do you think the game is too violent right now?' And all the coaches said, 'No,'" she said. "They feel like the equipment and the rules protected players."