Michael Andretti's operation, whose bid is supported by General Motors brand Cadillac, is the highest-profile contender of those who responded to the FIA's request for submissions to form an 11th F1 team.
Formula 2 outfits Hitech and Rodin Carlin had also submitted applications, along with start-up Asian effort LKYSUNZ.
Although there is still no official information from the governing body concerning which new teams, if any, will be accepted, Motorsport.com's sister title Motorsport-Total.com understands that only the Andretti bid has reached the final stage.
Formula 1 retains the final say on the admittance of a new entry to the grid, with CEO Stefano Domenicali repeatedly stressing that an additional team is not needed unless it brings additional value, while incumbent teams have been cold on the prospect of Andretti expanding its IndyCar and Formula E outfit into grand prix racing.
They believe the current $200m dilution fee that any new team would have to pay to join the grid is insufficient compensation, with opposition to Andretti's entry reaffirmed by several team bosses in Singapore.
An announcement from LKYSUNZ on Friday claimed that it was prepared to pay a dilution fee of $600 million, thanks to backing from a new billionaire investor from Florida.
This was met with surprise by employees of existing F1 teams amid speculation that LKYSUNZ staff have been informed it has been turned down by the FIA, prompting them to apply for jobs elsewhere.
Information uncovered by Motorsport-Total.com suggests that LKYSUNZ, Hitech and Rodin Carlin have all been informed that their submitted information was not sufficient for a positive evaluation, although the FIA would not officially confirm this when asked on Friday.
LKYSUNZ CEO Benjamin Durand said: "We are still in dialogue with the FIA. But I can't go into details at the moment because we are bound by an NDA which we respect."
It is understood that LKYSUNZ submitted new documents in the hope that the FIA would revise its assessment, but this is not expected to happen as the deadlines stipulated in the FIA tender have passed and the rejection is said to be final.
Why LKYSUNZ, Hitech and Rodin Carlin were rejected is not known at this point. To receive a positive decision in the FIA application process, new teams must not only prove that they have sufficient financial resources but also demonstrate a plan on how the project will be environmentally sustainable in order to achieve net zero CO2 emissions by 2030.
In addition, they had to present how the project would achieve a positive social impact, with staff diversity a focal point.
LKYSUNZ envisages a headquarters in Southeast Asia, most likely in the greater Kuala Lumpur area in Malaysia, which would pave the way for entirely new engineers and mechanics to enter F1.