New Zealand-based Rodin Cars says its application to enter Formula 1 has been rejected by the sport's governing body.
The company proposed building its cars in New Zealand and planned to reserve one of its two race seats for a female driver.
Andretti Global is expected to be the only bid that will be put forward by the FIA for consideration by F1.
However, F1 officials are likely to turn down the American application to become an 11th team on the grid.
Rodin is the majority shareholder in established feeder series operator Carlin, which runs teams in Formula 4, Formula 3 and Formula 2.
In a statement, Rodin's Australian founder David Dicker said the company was "financially equipped to fully fund" its F1 ambitions and would have pursued a potential collaboration with Ferrari.
Dicker added: "Rodin Cars participated in the recent FIA process aimed at gaining entry into the prestigious Formula 1 world championship - unfortunately, our bid was not successful.
"Recent information suggests, as anticipated from the outset of this process, that the only successful applicant will be Andretti Global."
Britain's Jamie Chadwick, who won the all-female W Series three times, would have been a candidate to fill the Rodin seat, had the bid been approved.
Chadwick, 25, has been racing in the IndyCar feeder series Indy NXT in the United States with Andretti Autosport, but she does not have a super-licence to enter Formula 1.
The sport has not had a female racer since 1976, but last week Britain's Jessica Hawkins became the first woman in almost five years to test an F1 car.
The FIA, motorsport's Paris-based governing body, opened a formal application process in February for teams interested in joining in 2025, 2026 or 2027.
Andretti Global, run by former F1 driver Michael Andretti, son of the 1978 world champion Mario, joined forces for a bid with US car giant General Motors' luxury Cadillac brand.
If Andretti Global got the go-ahead to join Formula 1, the team would look to secure at least one American driver.
Other bids include British racing team Hitech, backed by Kazakh billionaire businessman Vladimir Kim.
This story first appeared on the BBC