Elsewhere, Aston Martin are also known to be keen, with Newey having been given a 'secret' tour of their factory back in June, with recent reports even suggesting that a deal has been done between the two parties.
If that is true, it could be because of one distinct advantage that Aston Martin holds over their Newey competitors.
This advantage was recently discussed on the Sky Sports F1 Podcast by pundit and pit lane reporter Ted Kravitz.
Kravitz believes that a former Red Bull ally of Newey's - who is now at Aston Martin - could make a move to the Silverstone-based outfit very appealing, even suggesting that Newey may have held talks with said individual over the switch.
"You look at the investment that's already happened at Aston Martin, you look at their factory. He's already got Dan Fallows, who he worked with successfully at Red Bull, to be there with him," Kravitz explained.
"I would imagine he would have definitely talked to Dan Fallows and asked, 'What is this place that I'm coming to? What's it like?'
"I asked Dan Fallows about this in Hungary actually, whether he'd be happy with Newey joining him. Fallows said, 'What you have to understand is that Adrian is a relentless, unstoppable Formula 1 competitor, and I would be amazed if he didn't join another team, and I would certainly welcome working with Adrian again at Aston Martin'."
Kravitz continued, explaining that with the team already in place at Aston Martin, Newey could be the figurehead they need to drive them towards success.
“We've all had discussions with various people at Aston Martin about what you can offer someone like Newey," he continued.
"You can say, 'just come in, be a figurehead, sprinkle your magic dust here and there, put our people on the right path, and we think we've got the ability to do the rest with Fallows and the team that are already there'.
"It's a judgment call for Newey, where he wants to feel happy ending up at and the current leader, if we're to believe the rumors, is Aston Martin - but it could be any of those teams."