The suspended 26-year-old was purportedly photographed at a London airport, sparking speculation England was rushing him to Australia in the wake of the visitors' 10-wicket loss at the Gabba.
A photo widely shared on social media apparently shows Stokes walking through Heathrow Airport with large equipment bags.
But the England and Wales Cricket Board (ECB) quickly dismissed the rumour he would join the team for Saturday's second Test, saying he was instead paying for his own flights to visit family in New Zealand.
"The ECB is aware that Ben Stokes is making a private trip to New Zealand to spend time with his family. His travel arrangements have not been arranged by the ECB," a statement read.
"He is not on his way to the Ashes, England Lions or any other official training camps with the England set-up."
Stokes may get some playing time under his belt in New Zealand, however, with provincial team Canterbury confirming it had been in "initial discussions" with his representatives.
"The CCA Board and New Zealand Cricket will independently be considering this issue in the near future but, until then, we are unable to provide any more detail on the status of the deliberations," Canterbury chief executive Jeremy Curwin said in a statement.
Stokes was left off the plane for the tour after an incident outside a Bristol nightclub in September that left a man in hospital with facial injuries.
He was arrested before being released without charge and police and the ECB are both still investigating the incident.
Australian fans should not let their guard down just yet though.
Perth, the venue of the third Ashes Test on December 14, is about an eight-hour flight from New Zealand, putting the all-rounder within easy reach should he be cleared to join the team.