The current deal that runs from 2021 and 2025 was negotiated by former F1 CEO Chase Carey in what was regarded as a new spirit of cooperation compared to the often confrontational debates of the earlier Bernie Ecclestone era.
Preliminary discussions have already begun over the next Concorde, the first on Stefano Domenicali's watch as F1 CEO, even though it won't come into force until 2026.
Maffei says negotiations are much more straightforward these days due to an improved relationship between F1 and the teams, with all parties realising that the overall revenue pie is getting bigger.
"Historically, the Concorde Agreement was a snot-gobbling fight, and never got signed until after the season had already ended," said Maffei at an event hosted by Goldman Sachs.
"And they were operating backwards on what they were getting paid. We got it done this time. We're trying to change the dynamic, and I credit first Chase Carey and now Stefano with changing the dynamic with the teams, where we are far more aligned.
"That doesn't mean they want to pay us more, but they all agree on the value that we're doing together, and that growing the pie has been a positive thing for everybody. And providing stability and certainty about where we're going is a benefit to them.
"You've seen the value of F1 rise dramatically as we've grown EBITDA [earnings before interest, taxes, depreciation and amortisation].
"But the reality is the teams' valuations have increased much faster. They see the benefit of the regime that we've together created, they see the benefit of extending that deal."
Maffei says that an early agreement for 2026 will provide stability that will help both F1 and the teams to conclude long-term sponsorship deals and so on.
"What we're basically talking about is an early renewal of a deal that is very similar to the terms that they have today," he said.
"Why do we think that's a benefit? I think we can all sell sponsors, we can sell broadcasters, we can sell all people on the certainty of the sport, and you de-risk any of the potential in the future.
"I think they [the teams] have the opportunity to go out and sell the same sponsors on those ideas. So all of that is why everyone sort of wants to extend the current regime. And I think we've seen good interest in that."
Maffei noted that the overall percentage of F1 revenue that is shared with the teams has gone down, because as per the current Concorde F1/Liberty earns more on a sliding scale as overall revenue rises.
"If you look over the last five years, that percentage [paid to the teams] has gone down," he said. "That's largely due to the fact that there is a number at which we kick into a higher percentage.
"We said we would guarantee 'X' amount of payouts, but above a certain percentage, we're betting on ourselves. And if we get to that percentage of pre-team EBITDA, we'll take a larger split.
"What's happened as we've grown the sport is that the amount above that split number has grown, so our share has grown."
Regarding the next Concorde, he said: "I don't anticipate a major change in how that works. There will probably be something along the same lines, and we'll have an incentive to grow the business.
"They [the teams] have grown EBITDA dramatically. We've just because of the success and believing in the product and believing in ourselves been able to grow it faster, and I expect that it's going to be a similar construct in any kind of Concorde extension."
