An FIA spokesman confirmed the matter was on the agenda along with other sporting regulations for the virtual F1 commission meeting that includes the governing FIA and commercial rights holder.
Six of the 10 teams need to vote in favour, with further discussion expected, but some bigger outfits have indicated they will not block the proposal.
"It feels like there are two groups in Formula 1 at the moment. The teams from six to 10 are in as hard a fight as one to five," said Christian Horner, the boss of champions Red Bull, after last weekend's Chinese Grand Prix.
"It’s one of those things where you’ve just got to run the numbers and look at the analytics to say what would it actually change? I’m impartial to it unless of course you’re paying points money."
The current scoring system, in place since 2010, awards points to the top 10 only in a 25-18-15-12-10-8-6-4-2-1 sequence. The proposal would change that to 25-18-15-12-10-8-6-5-4-3-2-1 sequence.
After five races this season, three teams have yet to score while Red Bull-owned RB have managed only seven points and Haas five. The top half are in a league of their own, with dominant Red Bull on 195 already and even fifth-placed Aston Martin on 40.
If the points were handed out to 11th and 12th finishers, every team would have scored with Sauber and Renault-owned Alpine both on two and Williams on five.
"I'm not against," Ferrari boss Fred Vasseur, who was previously at Sauber when that outfit raced as Alfa Romeo, told reporters.
"I perfectly understand sometimes the frustration that you are doing a mega weekend but if there is no DNF (retirement) in front of you then you finish P11 and the reward is zero."
Laurent Mekies, the RB team principal, told www.autosport.com that the current situation was hard to explain to sponsors.
"If you look at the level of competitiveness of the top five teams and the reliability level of the cars, it means that most of the race you're battling theoretically for zero points, and we don't think this is right," he said.
Haas's Ayao Komatsu saw no downside. "Currently, we have three teams with zero points and I don't think that's good for the sport," he said.
Drivers have been divided on the matter, with some pointing to the special feeling of finishing in the top 10 and others seeking more radical action.
"Maybe give points to everyone," said Haas's Kevin Magnussen. "50 points to P1 and then spread it out. It won't change anything at the top, but would make the races more interesting for the bottom five."
