Michael Andretti (60) has already announced plans for an American bid with the support of General Motors brand Cadillac, but the commercial rights holder and most of the 10 existing teams have sounded lukewarm on expanding the grid.
The teams are concerned about diluting their share of the revenues while Liberty Media-owned Formula One Management (FOM) has been increasingly at odds with Mohammed Ben Sulayem, president of the governing FIA.
The FIA said it sought to identify one or more new teams interested in joining in 2025, 2026 or 2027.
Those proceeding to a formal application process must pay a fee of $300,000 to cover due diligence checks carried out by the governing body.
The deadline for submission of formal applications was expected to be April 30 with any decision by June 30.
Criteria included a detailed business plan for the first five years and, for the first time, proof of sustainability and how the team intended to "achieve a positive societal impact through its participation in the sport."
The FIA said there was a high level of interest but recognised FOM had a say and "may also impose additional selection criteria/conditions".
While the FIA ultimately owns the rights to the championship, it signed them over to FOM in a 100-year deal in 2001 as part of a separation of commercial and regulatory activities.
The championship is limited to a maximum 12 teams up to and including the 2025 season. The sport will have a new power unit from 2026, when Audi will also enter after taking over the existing Sauber team.
"The growth and appeal of the FIA Formula One World Championship is at unprecedented levels," said Ben Sulayem.
"The FIA believes the conditions are right for interested parties, which meet the selection criteria, to express a formal interest in entering the Championship."
