The Brit has been with the reigning constructors' champions since 2006, and has since designed championship-winning cars for the likes of Max Verstappen and Sebastian Vettel.
His decision to depart the Milton Keynes-based outfit will likely have a significant impact on the team, given that he is free to sign with one of their major rivals.
If that were to happen, Newey would link up with former world champion Fernando Alonso, something the Spaniard has admitted would be an enticing prospect.
Despite ongoing speculation surrounding his future, Newey appeared to be in a relaxed mood as he was filmed driving his Aston Martin Valkyrie sports car - which was manufactured in collaboration with Red Bull - in the UK last week.