Michael Andretti said on Sunday he expects to know in mid-July whether he can enter Formula One with a new American team from 2025.
Andretti, son of 1978 world champion Mario, told Sky Sports television at the Miami Grand Prix that the paperwork was being submitted to the governing FIA this week.
Andretti Global and General Motors announced in January that they planned to compete using the Cadillac brand and employing at least one US driver.
"That's our goal, We're working on it," Andretti said of the bid.
"We have a process that we're in the middle of with the FIA and we're submitting our paperwork this week, and hopefully get an answer middle of July. We're making good progress."
Andretti, a former McLaren F1 driver and 1991 CART champion, confirmed he was targeting 2025 and said work was underway already.
"We're building a team as we speak," he added.
Renault-owned Alpine have said they will supply the engines if the Andretti Cadillac team wins approval from the FIA and commercial rights holder Liberty Media.
Other Formula One teams have been lukewarm towards expanding the grid, wary of diluting the overall pot of revenues.
Some also feel the current $200 million entry fee, which would be shared among the existing 10 teams as compensation, is not enough.
The FIA started a formal application process in February, seeking to identify one or more new teams interested in joining in 2025, 2026 or 2027.