The FIA may have to force the halo through on safety grounds to get the cockpit protection device on Formula 1 cars in 2017, Autosport understands.
The latest Strategy Group meeting takes place in Geneva on Thursday, with the halo's potential introduction one of the main items on the agenda.
The indication is the vote will go against the halo unless FIA president Jean Todt can allay the concerns the device lacks maturity and is being rushed through, despite passing tests.
Under the regulations its introduction now requires a unanimous vote from the Strategy Group, which is only an advisory body, before being referred onto the F1 Commission, where again unanimity would be required.
Todt and Bernie Ecclestone possess six votes each in the Strategy Group, while the six teams involved have one vote apiece.
It only requires one dissenting voice within the Strategy Group, and again within the F1 Commission where all the teams are represented, for the halo to be shelved.
The FIA could decide to play its trump card in such situations and declare the halo will still be a part of the technical regulations for 2017 on safety grounds.
Autosport understands Ecclestone is among those in opposition, and that behind the scenes he has been lobbying the teams to vote against it.
Ecclestone would appear to have support, primarily from Red Bull - prime-mover behind the alternative aeroscreen concept - as team principal Christian Horner recently suggested he is not in favour.
"I'm not a big fan of the halo and the limitations that it has. I certainly wouldn't vote in favour at the moment," he said.
Force India is believed to be another team poised to say no, while McLaren and Williams are also understood to have considerable reservations.
Mercedes motorsport boss Toto Wolff admitted recently he has yet to make up his mind.
"Whatever can be done for the safety of the drivers needs to be done, even if it looks disgusting," said Wolff.
"I don't think it looks Formula 1, and I don't think it makes the sport, the cars and the drivers appear spectacular.
"But all that doesn't count because safety comes first. Is it the safety tool we need in order to protect the drivers more?
"My personal opinion is we need to look at all the studies, discuss them and come to a decision that it is either a good thing, or it's a good thing but not where it should be yet, or we don't like it for safety reasons."
Lewis Hamilton, who previously derided the halo as "the worst-looking modification in F1 history" has softened his stance.
A FIA presentation for the drivers at last weekend's Hungarian Grand Prix impressed Hamilton, who revealed the halo would improve safety "by 17%".
He added: "It looks terrible, but if one of us is going to have a 17% better chance of surviving in a serious incident..."