With the series in a strong position and with growing global interest, all parties would benefit from an early signing of the new contract, Maffei said.
The current deal, covering 2021-25, was signed on the watch of former F1 chief Chase Carey and tHis successor, Stefano Domenicali, will be next in charge.
“We still have a few years to implement the Concorde agreement,” Maffei said on a conference call with Wall Street analysts.
“But I think there is a consensus between the teams, the FIA and ourselves that now might be a good time to try to strike while the iron is hot, to renew and extend the Concorde agreement.
“Of course there is no obligation to do so. There is certainly no risk in not doing so.”
Maffei noted that the last negotiations were at an advanced stage before the renewal was confirmed.
“As you may recall, we went all the way to the end,” he said. “Historically, in many cases where fleets have operated without the Concorde agreement, they’ve basically just shaken hands and then done the deal after the period when the new Concorde was supposed to start.
“We’re hoping this time around, we’re able to change that dynamic, partly because of the way Chase and Stefano changed the team dynamic.
“I hope we have a more positive relationship where everyone sees the benefit of moving early and providing certainty to all involved.”
F1 team bosses agreed an early Concorde delay would be positive as it would give them more clarity in the long term, but stressed that negotiations should be kept out of the public eye.
“I think the most important thing is to have this conversation behind closed doors,” Mercedes team principal Toto Wolff said.
“I think if we have long-term, long-term partnerships and contracts, like Concorde, the longer the better, I think that’s true for all of our businesses. But we’re at 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. There’s no way it’s going to be live and controversial.”
“F1 has never been in such a strong position,” said Red Bull boss Christian Horner. “I think Liberty is doing a great job with the sport, we’re seeing new markets, new growth, new fans and new fan bases.
“There will always be a debate between teams and commercial rights holders over who deserves more value. As Toto said, expect a duel that will undoubtedly take place behind the gate.
“But I think longevity is in everyone’s best interest, to have a solid sport that has a clear direction for the future, what its goals are, and what technical regulations and sporting regulations and financial regulations we want to have for the future, in the next few years Keep making the game better, more engaging and inclusive.”