Andretti officials are "not very smart" to denounce the existing Formula 1 team bosses as "greedy", the sport's CEO Stefano Domenicali has warned.
FIA president Mohammed Ben Sulayem has instigated a process to potentially allow two new team entrants on the grid - and is openly backing the Andretti-Cadillac bid.
Various existing F1 teams, however, are diametrically opposed to the move.
"What upside is it bringing? There is just risk, no benefit," said Haas boss Gunther Steiner.
"Five years ago, you could get teams for nothing but nobody wanted them and they went out of business. Now, all of a sudden, everybody wants a team."
Indeed, F1 is now thriving in the Liberty Media era - but Steiner says an eleventh team threatens that.
"If you put an eleventh in and we get a little bit of a dip in the economy or something, all of a sudden maybe people are maybe struggling to survive," he said.
The boss of a much bigger and more successful team, Red Bull, agrees.
"Red Bull was first Jaguar, which used to be Stewart-Ford," said boss Christian Horner. "Mercedes' history goes back to Honda, BAR, Tyrrell. Aston Martin was Jordan.
"This has been the procedure for many years," he insisted. "I have nothing against Andretti, they are great people and Cadillac is a great brand.
"But we need to come up with criteria that doesn't detract from the value of teams, especially the smaller ones."
Former F1 driver turned veteran British broadcaster Martin Brundle defended the existing teams' point-of-view.
"There have been times when they have lost tens and hundreds of millions of dollars," he said. "So they're saying 'Just because things are going well, we won't just let other teams into the club and reduce our share'."
At the end of the day, it is expected that the financial side will settle the issue either way. As for Domenicali, he questions Michael and Mario Andretti's strategy of calling the existing teams 'greedy'.
"No one can pressure us to make a decision just because someone is screaming the loudest," said the Italian.
"There are groups of people like Mario and Michael Andretti who want to get into F1 and are saying it loudly, but to say that the teams are just greedy is not a very smart tactic.
"There are other people who are quieter and also want to come into Formula 1," Domenicali added. "So there is a process to be respected and we will work with the FIA to ensure that."