The all-rounder wasn't included in England's Ashes squad due to an ongoing police investigation.
"Canterbury Cricket can now confirm that they have been in initial informal discussions with Ben Stokes' representatives regarding his potential availability for Ford Trophy and Burger King Super Smash competitions", they said in a statement.
An image that claimed to show him at the airport began doing the rounds on social media late Monday, sparking speculation that he was flying Down Under to take part in the Ashes.
New Zealand Cricket spokesman Richard Boock said his organization "has yet to receive a formal request regarding Ben Stokes".
Ben Stokes is reportedly heading downunder - but it won't be to join the England cricket team in Adelaide.
The England and Wales Cricket Board (ECB) said the former worldwide was making a private trip to spend time with his family, but Canterbury have confirmed that they've entered into informal negotiations with the 26-year-old.
Travel arrangements have not been arranged by them.
"He is not on his way to the Ashes, England Lions or any other official training camps with the England set-up".
Stokes, 26, remains the subject of a police investigation after a brawl outside a Bristol nightclub, with the England and Wales Cricket Board having declared it was waiting for that process to be finalised before deciding on any disciplinary measures.
Stokes moved to England with his parents as a 12-year-old after his New Zealand rugby league worldwide father, Ged, took up a coaching job in Cumbria.
"As and when there are any further developments we will of course release further statements".