Andretti recently did himself no favours, however, when he turned on the teams in an interview with Forbes.
“It's all about money,” said Andretti. “First, they think they are going to get diluted one-10th of their prize money, but they also get very greedy thinking we will take all the American sponsors as well.
“It's all about greed and looking at themselves and not looking at what is best for the overall growth of the series.”
F1 boss on Andretti project
Speaking with driver-turned-commentator Martin Brundle in an interview for Sky Sports, Domenicali has made it clear that Andretti was unwise to be so vocal.
“We are very welcoming of everyone that is bringing value to the racing,” Domenicali said.
“I think we need to respect everyone.
“But in my view [it is] not smart to say that teams are greedy,” he added.
“There are others that are much less vocal that would like to come into Formula 1, so there is a process to respect and we will make sure together with the FIA that the process will be respected.
“There are a lot of dimensions to consider and we don't have to overreact because someone is pushing the system.
“The process will be done seriously in the right way someone is shouting and someone is not shouting.”
The argument against new teams
An argument against allowing an 11th team into F1 is the impact it will have on the 10 who currently share the prize money pot.
There is a $200 million figure payable for a new entrant with that money divided equally among the incumbent competitors to offset any drop in income that follows.
However, that is a one-time payment leaving teams concerned the increased competition will, long term, result in their prize money income dropping.
It is for that reason that the likes of Andretti entering F1 need to demonstrably increase the value of the sport; doing so increases its income and therefore offsets the fact prize money would be spread across 11 rather than 10 teams.
Earlier this month, the FIA formally opened its Expressions of Interest process, outlining a number of areas new entrants must cover, including financial, sporting, environmental, and social expectations of the new operation.
New teams in the recent past
The last team to enter Formula 1 was Haas, which joined the grid at the start of 2016.
Prior to that, F1 opened itself up to four new teams for the 2010 season, though only three of those made the grid.
The USF1 project proved to be a stillborn while regulation changes surrounding the sport's finances meant Virgin (Manor), Hispania (HRT), and Lotus (Caterham) all struggled at the back of the grid.
Hispania lasted three seasons before closing its doors in 2012 while Caterham hung on for another two years before it also went bust. Neither team scored a world championship point.
Virgin, which became Marussia and finally Manor, held on until the end of 2016, scoring three points in six seasons before finally closing its doors.