'Speed TV' claims that the body, which approves the teams' recommendations for things like rule changes, will no longer grant a vote to every team.
Instead, there will be just six team votes, along with a vote for the FIA, one for Bernie Ecclestone, and one each for five grands prix.
It is understood that McLaren and Prodrive missed out because the FIA deems Williams to be the senior British team.
Similarly, under a one-vote-per-nationality rule, Toyota and Super Aguri were passed over in favor of senior Japanese entrant, Honda.
FIA president Max Mosley said: ''What we're proposing is one team from each country. I think we would have to take the most senior team.''
It means that Renault (France), Ferrari (Italy), BMW-Sauber (Germany) and Red Bull (Austria) have votes, with Toro Rosso and MF1/Midland also missing out.
The matter, by fax vote, is due to be ratified by the FIA's World Motor Sport Council later this week.