He was given a non-objection certificate by the European Central Bank last week to play domestic cricket although he remains under suspension from the England team.
The England and Wales Cricket Board (ECB) said the former global 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.
New Zealand side Canterbury say they have held talks with Ben Stokes after the England all-rounder was seen at Heathrow airport on Monday.
There has been no police update since the all-rounder was arrested and released under suspicion of causing actual bodily harm in September.
British media then reported that Stokes is travelling to Christchurch, New Zealand to visit his parents Barbara and Gerard Stokes.
Canterbury Cricket chief executive Jez Curwin didn't rule it out as a possibility, telling reporters "we'd be delighted to have him come and play for us if we ever got to that stage".
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England may fast-track Ben Stokes into the Ashes if he avoids police charges. "His travel arrangements have not been arranged by the European Central Bank", it said in a statement.
If he does play, it will mark the New Zealand-born cricketer's first competitive game since England's one-day global against the West Indies on September 24.
Stokes is travelling to New Zealand, but the European Central Bank confirmed to Sky Sports News on Monday that the 26-year-old "is not on his way to the Ashes, England Lions or any other official training camps with the England setup".
But Press Association Sport understands that the England and Wales Cricket Board has a contingency in place should Avon & Somerset Police clear the 26-year-old.
England suffered a 10-wicket loss in Brisbane, with the second Test beginning in Adelaide on Saturday.