The matter has arisen at a time of heightened awareness of the off-the-field behaviour of England players, following Ben Stokes' arrest on suspicion of causing actual bodily harm during a fracas outside a Bristol nightclub in September.
Half-centuries from Bancroft and fellow opener David Warner saw Australia to 114-0 at the close. "Both Bancroft's group and the England players continued drinking together at the Avenue bar in Perth".
Jonny Bairstow has come under investigation for allegedly head-butting Cameron Bancroft in Perth at the start of England's Ashes tour.
Cameron Bairstow is in hot water over the allegations.
Fox Sports Australia is reporting Bairstow headbutted Bancroft, while other versions suggest it was more low key and a case of tomfoolery gone awry.
England were in Perth for a two-day match against a Western Australia XI, their first outing of the tour before heading to Adelaide and Townsville for four-day matches against a Cricket Australia XI.
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"Following an initial conversation with Jonny Bairstow tonight, we understand the context and will follow up with England players and management after the Brisbane Test". Bairstow is believed to have apologised at the time.
No police report has been filed as of yet and it remains to be seen if the incident will be reviewed by the European Central Bank.
Bancroft, who did not play in the match, was at that stage just a fringe contender for the Australian team and joined some of his state team-mates along with a large number of England players at The Avenue bar.
Last month Bairstow was one of three England players fined by the European Central Bank for "unprofessional conduct".
England coach Trevor Bayliss flagged the prospect of an Ashes curfew following the Stokes fracas but made a decision to give his players free rein, trusting them to enjoy themselves in a sensible manner.
There is an acceptance within the European Central Bank that they can not keep the players confined to hotel rooms on tours that last for weeks on end but the last thing they needed was more accusations that any of their players had done anything wrong.