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The Test vice-captain was included in England's 16-man Ashes squad led by skipper Joe Root announced earlier yesterday, despite injuring his hand in the incident that led to his arrest in Bristol on suspicion of causing actual bodily harm.
The 26-year-old was released without charge on Monday but remains under investigation.
In the video posted by the Sun, which headlined its front-page splash 'Hit for Six', Stokes appears to be fighting with two men, one of whom is holding a bottle.
"There is an ongoing police investigation, which will look at all available evidence, and we do have to respect that process."
He was omitted from England's series-clinching ODI win against West Indies at The Oval after being arrested in the early hours of Monday morning.
His arrest followed England's win in the third ODI in the southwestern city of Bristol on Sunday.
"As it currently stands, he is (Test) vice-captain pending any disciplinary action," ECB cricket director Andrew Strauss told reporters.
Avon and Somerset police said Tuesday they had been called to an incident in the Clifton district of Bristol at around 2:35 am (0135 GMT) on Monday.
"The other night a few guys being out was very unprofessional in the middle of a series," the Australian added.
Both Bayliss and Strauss are wary of curfews, with the ex-England skipper saying they believed in "treating people like adults".
- 'Cancel England's flights!' -
But Strauss conceded Stokes's incident could lead to a re-think, a point emphasised by England limited-overs captain Eoin Morgan after Wednesday's win.
"We'll have to put something in place that doesn't leave us in the position we are at the moment," said Morgan.
Stokes, potentially just one on-field offence away from a Test ban under the International Cricket Council's code of conduct, is seen as vital to England's chances of retaining the Ashes in Australia, which start with November's first Test in Brisbane.
Former England batsman Kevin Pietersen, jokingly suggested the Sun's story spelt the end for the current side's Ashes hopes, tweeting: "Oh No! Just seen tomorrow's front page & video! Cancel England's flights please!"
England great Ian Botham, speaking after the squad was announced but before the video was published, said he hoped fellow all-rounder Stokes was "the innocent party".
Botham, however, added: "You cannot be wandering the streets at 2:30 am."
Stokes, sent home from an England Lions tour in Australia in 2012/13 for flouting a ban on late-night drinking, told The Times in an interview published on Saturday he enjoyed a couple of beers after stumps.
"We're grown men, go out for dinner, have a few pints," he said.
"I'm 26, not 14. I don't have to drink Diet Cokes with dinner.