Ferrari driver Sebastian Vettel and Red Bull team boss Christian Horner say the 'halo' head protection system is not yet ready for introduction.
Vettel tried the latest version of the device in practice at the British Grand Prix and said it "needed some further running".
Horner added that the device should not be "rushed through" and said he would not vote for it to be used in 2017.
Governing body the FIA wants to introduce the halo next year.
However, the halo is yet to be formally approved.
FIA F1 director Charlie Whiting has made it clear to teams in technical meetings they should expect to run the halo in 2017 and they are designing their new cars so that is possible.
However, the halo must first be approved by a three-stage process: the strategy group of leading teams, the FIA and F1 commercial boss Bernie Ecclestone; the F1 Commission, on which sit representatives of all teams, sponsors, circuits, tyre suppliers, plus the FIA and Ecclestone; and the FIA World Council.
Sources have told BBC Sport that, in addition to Horner, Ecclestone, Mercedes F1 boss Toto Wolff and Williams deputy team principal Claire Williams also have misgivings about the device, which is designed to protect drivers from impacts with large flying objects.
Horner said: "I am not a big fan of the halo and the limitations it has. It is an inelegant solution to the problem it is trying to deal with.
"I would prefer there to be more research time taken to do the job properly rather than rushing something through that may have other consequences. I certainly wouldn't vote in favour of it."
The Grand Prix Drivers' Association, of which Vettel is one of three directors, is in favour of increased head protection for drivers and would like to see something introduced as soon as possible.
But after Vettel ran the device for one lap in Friday practice, he said he had concerns about the sensations it gave the driver.
"Forward visibility was fine," the four-time champion said. "But it was quite a bit on top of you, (even if) you are not looking at the sky all the time.
"It needs some further running. I know the decision is up fairly soon. I don't know what the results are on the actual research.
"It is clear what it is made for and what it is supposed to do, but we just need to make sure we introduce something safer in all circumstances and we don't have any compromises."
The FIA has promised teams a decision on the halo by the end of July.
Red Bull were proposing an alternative device called the 'aeroscreen' but that failed FIA tests, which involve a wheel being fired at the device at 250km/h (155mph).
The team have now stopped work on the aeroscreen, preferring to put more resources behind their 2017 car design as a result of the major rule changes that will see wider cars aimed at reducing lap times by about four seconds.