Ben Stokes would be welcomed back to the England squad “with open arms” after touching down in New Zealand to get himself match fit for a possible Ashes call-up.

Saturday’s pink-ball second Test in Adelaide – a chance to draw level with Australia after the 10-wicket defeat at the Gabba – remains the focus for Joe Root’s tourists but looming over their preparations was the arrival of Stokes in the southern hemisphere.

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Met by his parents and a gaggle of news crews at Christchurch airport, Stokes said he was looking forward to some family time and “working on my golf swing”. But behind the scenes the provincial side Canterbury were holding a board meeting to decide whether to sign the suspended all-rounder on a short-term deal ahead of a possible comeback on Sunday.

Though still unavailable for England selection following his arrest in Bristol on 25 September, Stokes, after a broken finger, is trying to get himself in the best possible physical shape should both the legal case and any cricket punishment go his way. The third Test at Perth from 14 December is a mooted target but that would need a retrospective punishment.

Root’s players in Adelaide were – as the England and Wales Cricket Board less convincingly claims to be – caught unaware by Stokes’s movements. Nevertheless, the word from the camp is they want their talisman alongside them on the Ashes frontline.

“As an England team we’d like to see him here,” said Woakes. “As a player, as a friend. I’d like to see him here. No one likes to see what he’s been through. Of course we’d have him here with open arms, I’m sure. Ben’s a world-class cricketer and he’d make any team in the world better so it’d be silly of us to not open it up for him to come into the squad.

“It’s good news for the squad. It doesn’t mean he’s arriving anytime soon but at the same time it means he’s a little bit closer, I suppose. Fingers crossed he can get out there, play some cricket, get some form and who knows? Obviously there’s still a police investigation going on, so that’s completely out of our hands.”

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England’s contortions over the matter have dominated the news agenda in Australia. Their former opener, Michael Slater, accused Andrew Strauss, the team director, on local radio of deception after signing off Stokes for domestic cricket late last week and before Monday’s assertion that there was no update.

Another past player, Mike Hussey, told the Cricket Australia website it was a good move to get Stokes primed in New Zealand in the event of being cleared, while Shane Watson, who featured in the 2013‑14 series, said the all-rounder should miss the whole series regardless in an interview with Sydney’s Daily Telegraph.

There will be divided opinions at ECB board level, where the public image of English cricket is fretted over more greatly than a team simply desperate to defend the Ashes. With Jonny Bairstow’s “weird” head-butt greeting for Cameron Bancroft four weeks ago having seen the squad issued with a midnight curfew, these are sensitive times.

Nathan Lyon, the off-spinner who took five English wickets in Brisbane (including four left-handers), spoke at Australia’s training session and switched from being agitator-in-chief to respectful of England, declining questions on Stokes and Bairstow and tipping a response.

“They’re a classy side, with a very exciting young captain, Joe Root,” said Lyon, whose Australia side have four wins from four in day-night Test cricket. “The pink ball is going to suit their bowlers. It’s one of the dangerous periods when teams are far down or in turmoil. I don’t think they are, but if you don’t respect teams that’s when they can come back and bite you.”

Alastair Cook was among the names listed by Lyon as threats and, after a concerning first Test that saw him nick off for two and then be suckered into a pull shot on seven in the second innings, the former captain netted alone at the ground during a rest day for England.