The current Concorde Agreement, F1's crucial three-way commercial deal between the commercial rights holder (Liberty Media-owned FOM), the FIA and the 10 teams covers the 2021-2025 period.
With two more years remaining beyond the current season, there's no rush to thrash out a fresh deal, but in a recent call with Wall Street analysts Liberty Media president Greg Maffei said he was keen to "strike while the iron is hot" and use F1's strong momentum to agree to new terms well ahead of time.
"We have several years left to run on the Concorde Agreement," Maffei said.
"But I think there's a consensus among the teams and the FIA and ourselves that now might be a good time to try and strike while the iron is hot and renew and extend the Concorde Agreement."
McLaren CEO Brown thinks it would be beneficial for the stability of the series to get a new deal done "sooner rather than later" and believes a new deal could be little more than a "rinse and repeat" of the current terms.
"I think everything's working great," he said. "If you look at the health of the sport, from a Liberty point of view, from the 10 racing teams’ point of view, the teams that want to come in, the promoters, the fans, the TV, so I'd like to see it get done sooner rather than later, just for the stability and longevity of the sport.
"I also think it's a little bit of a rinse and repeat. I think it's working. I don't think there's much to add or change to the existing agreement, so I don't think it needs to be a prolonged conversation either. I'd pretty much be happy with a rinse and repeat with a few tweaks here and there.
"There's things in the digital age that have advanced since we did the last agreement that I think need to be discussed. But I think for the most part, it's a solid agreement. It's working so we don't really need to fix what's not broken."
Haas' Gunther Steiner and Alpine team boss Otmar Szafnauer were also not against the idea of commencing formal talks in the near future.
"I think if you start now, you know how long these Concorde agreements normally take, so the earlier we start, the earlier we get to a conclusion," said Steiner.
"So, I'm not against this if FOM wants to come and propose to us what they want to do for the next five years, which is actually the next seven years now. I think we, as a team, are pretty happy to talk with them."
Sazfnauer added: "If FOM are willing to start talking with the teams and start an outline of what a new Concorde Agreement could be, then starting early, I don't see any downside with that."
Mercedes team principal Toto Wolff urged F1 to keep fresh Concorde discussions behind closed doors and steer it away from controversy.
"I think most important is to have these conversations behind closed doors," Wolff stressed. "If we have a long period of alignment and a contract, such as Concorde, the longer it goes, the better it is for all of our businesses, but we are in a very early stage.
"We haven't really started talking properly. That's going to happen soon. But it should happen in a constructive way, not maybe live broadcasted and creating controversy."
Red Bull's Christian Horner said he is looking forward "to the jousting that will no doubt take place" between all stakeholders over the additional value F1 has generated under Liberty Media's watch.
"Formula 1 has never been in a stronger position. I think Liberty has done a great job with a sport," he added.
"We're seeing new markets, new growth, new fans, and a new demographic of fans. There's always going to be that debate between the teams and the commercial rights holder of who should have the more value, and I look forward to the jousting that will no doubt take place, as Toto says, behind doors.
"But I think longevity is in the best interest of everybody, to have a settled sport that has a clear direction for the future, of what its goals and objectives are, together with the technical, sporting and financial regulations that we want to develop for the future, to just continue to make the sport better and more appealing and more inclusive over the coming years."
