Maffei suggests that all parties will benefit from the early conclusion of a new contract while the series is in a strong position and interest is growing worldwide.
The current deal, which covers the years 2021-25, was signed on the watch of former F1 CEO Chase Carey and the next one will be the responsibility of his successor Stefano Domenicali.
"We have several years left to run on the Concorde Agreement," said Maffei in a call with Wall Street analysts.
"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.
"There's certainly no obligation to do that. And there's certainly no risk if that doesn't get done."
Maffei noted that last time negotiations reached a late stage before a renewal was confirmed.
"As you may recall, we went right to the end," he said. "And historically, in many cases, the teams have operated without a Concorde Agreement, they've basically done a handshake and then completed the deal post the period when the new Concorde was supposed to start.
"Our hope is that this time, we'll be able to change that dynamic, in part because of the way that Chase and Stefano have changed the dynamic with the teams in particular.
"I hope we have a more positive relationship, and everybody sees the benefit of going early and providing certainty for all involved."
F1 team bosses agree that an early extension of the Concorde would be positive as it would give them longer-term clarity but stressed that negotiations should be kept out of the public eye.
"I think most important is to have this conversation behind closed doors," said Mercedes team principal Toto Wolff.
"I think if we have a long, long period of alignment and a contract, such as Concorde, the longer it goes, the better it is, I think 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 broadcast it and create controversy."
"F1 has never been in a stronger position," said Red Bull boss Christian Horner. "I think Liberty have done a great job with the sport, we're seeing new markets, new growth, new fans, a new demographic of fans.
"And there's always going to be that debate between the teams and the commercial rights holder of who should have the more value. And 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, and what its goals and objectives are, together with the technical regulations and sporting regulations 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."
