The Christchurch-born Stokes is on his way back to the city, ostensibly to visit family as the Ashes are being played out across the Ditch.
But Times reporter Elizabeth Ammon has suggested on social media that he will be playing domestic cricket here.
Ammon tweeted today: "The Times understands that [England team director Andrew] Strauss has given him the OK to play for Canterbury Cricket - they have limited overs competitions coming up starting 3rd Dec. More in tomorrow's Times…"
Canterbury coach Gary Stead told the New Zealand Herald that nothing has been confirmed.
"If it happened, a lot of water would have to go under the bridge," Stead said.
"There would need to be New Zealand Cricket and ECB [England and Wales Cricket Board] sign-off as well as our board, and being clear we were comfortable with that. We're not at that stage."
The 26-year-old Stokes, on a ban from the England side – an important distinction – for his part in what has been described as a street brawl during a night out, would be a big boost for a Canterbury side plagued by injuries, and currently sitting last on the four-day Plunket Shield ladder.
Extra reinforcements are coming for their Ford Trophy campaign, with promising paceman Ed Nuttall soon to return from injury, but a Stokes cameo would make him the best player in the competition - as the core Black Caps will be busy with international commitments.
Canterbury are the defending Ford Trophy champions, and kick off their title defence on December 3 against Otago in Rangiora, while their Twenty20 season gets underway shortly after, on December 14 in Christchurch.
Stokes averages 35.5 with the bat in List A cricket at a strike rate of 100, and a bowling average of 29.2.
The allrounder's absence from the England side has already been felt – the visitors were comfortably beaten in the first test in Brisbane, and he will want to remain in good touch before a possible return to the side.
Stokes is unavailable to play for England – but remains on full pay – while he and the ECB wait to discover if he will be charged following his late-night arrest in Bristol on September 25. Only then will his cricket disciplinary hearing take place.
The England and Wales Cricket Board confirmed Stokes' visit to New Zealand in a statement, saying: "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," it read.
"He is not on his way to the Ashes, England Lions or any other official training camps with the England set-up."
Sky Sport UK are reporting that the Christchurch-born player is flying to New Zealand to spend time with family.
