Autosport understands that over the recent Saudi Arabian Grand Prix weekend, Stroll presented pre-eminent F1 designer Newey with a big-money bid to move.
Although Newey has turned down opportunities to leave Red Bull since joining in 2006, most notably rejecting advances from Ferrari, such a statement signing would help Aston Martin owner Stroll fulfil his ambition of turning the Silverstone squad into a serial world championship winner.
He has already overseen the completion of a new factory, a 2026 works engine deal with Honda, signed key staff from Mercedes and Red Bull plus green-lit the build of a new wind tunnel.
But Aston Martin team boss Mike Krack reckoned he was already satisfied with a technical department that included former Red Bull head of aerodynamics Dan Fallows, performance director Tom McCullough, engineering chief Luca Furbatto and recent ex-Alpine signing Bob Bell.
Asked specifically by Sky Sports if Aston Martin had made an "astronomical" bid for Newey, Krack replied: "No... We have a very strong technical team with Dan, with Tom, with Luca. We were joined lately by Bob Bell. So, we're quite happy with what we have, at the moment."
While Stroll has built up the infrastructure at Aston Martin, he must still secure a driver line-up for 2025 and beyond.
Fernando Alonso has repeatedly opted not to publicly pledge his future to the team beyond the expiration of his current contract at the end of the year as berths at Mercedes and Red Bull remain viable.
Aston Martin could attempt an ambitious swoop for Max Verstappen, with the reigning three-time world champion said to be unsettled by the turmoil within the Red Bull F1 team hierarchy.
Signing Newey could have a major influence in Alonso and Verstappen's next move.
Red Bull advisor Helmut Marko told Autosport Newey was "highly demanded", adding that any offer from Aston Martin would be not the "last" presented to the Briton.
"Newey is a designer that is highly demanded. He is the one that everybody wants to have. I don't think it was the first offer and I don't think it will be the last offer that he got…
"To lose Newey is always a big disadvantage because then it means that another team would get him. In such a case he would take knowledge, but also unbelievable experience with him…
"He is like a cult figure so it's very important for young engineers as well. They come into the team because they want to work with Newey. Overall, it's a big gain to have Adrian."