Speculation leading into this weekend's Sao Paulo Grand Prix linked the American with the shock move, with some suggesting an agreement in principle has been reached between the parties.
Szafnauer has been a longstanding member of the management team for Aston Martin, having joined what was then Force India in 2009.
Meanwhile, Alpine has undergone a significant management restructure this year following the sudden departure of Cyril Abiteboul.
The latter joined the French manufacturer from the Suzuki MotoGP team and has been rumoured to be eyeing a return to the two-wheeled world.
Both Alpine and Aston Martin refused to comment on the speculation, dismissing it as such, before Szafnauer took to social media in an effort to hose down the claims.
“My Aston Martin team communications staff have correctly issued a spokesperson's statement to the effect that rumours linking me to Alpine F1 team are merely speculative conjecture and that they would not therefore comment further,” he stated.
“However, since the rumours have now been sensationalised on certain websites, creating a spiral of misinformation, l have taken the decision proactively to confirm hereby that the rumours are pure media speculation and not based on fact.”
Szafnauer's role at Aston Martin was questioned earlier in the year, when it became apparent the operation was in the market for a senior leadership figure.
It was announced in September that former McLaren team boss Martin Whitmarsh would take on the role of Group Chief Executive Officer of Aston Martin Performance Technologies, which oversees the business more broadly than the Formula 1 team.
Aston Martin is currently in the midst of a growth and development cycle following fresh investment from a consortium led by Lawrence Stroll.
That has seen a number of new recruits as the squad bolsters its staff, while Stroll recently broke ground ahead of an expansive new factory.
Aston Martin currently sits seventh in the constructors' championship, 38 points behind Alpine and AlphaTauri, having ended the 2020 campaign fourth.