In a statement the European Central Bank said: "At close of play in Brisbane today, we were made aware of allegations of an incident in Perth four weeks ago".
Bancroft celebrated his maiden half-century on Test debut while vice-captain Warner raised his 25th.
After Ben Stokes landed himself in trouble for brawling outside a bar in Bristol, England wicketkeeper-batsman Jonny Bairstow is facing an inquiry over an alleged incident that took place in a bar in Australia.
It's understood Bancroft did not instigate or retaliate to the headbutt and that the two respective groups remained at the Avenue Hotel in Perth after the alleged incident occurred.
Neither is the police involved nor have any official reports been made after the incident.
Australia's David Warner plays a shot against England during their Ashes cricket test in Brisbane, Australia, Sunday, Nov. 26, 2017.
Bairstow was reportedly quick to apologise after the incident, and there is no police involvement or official complaints.
Cameron Bancroft and David Warner scored unbeaten fifties as Australia raced to 114 for naught at stumps on day four chasing a target of 170 runs for a win in the first Ashes Test against England in Brisbane.
It is claimed there was an incident in a bar in Perth during England's pre-series tour match against Cricket Australia.
European Central Bank chief Andrew Strauss was spotted looking dejected late on Sunday in Brisbane after Bairstow was questioned about the matter.
England coach Trevor Bayliss said in the aftermath of Stokes' arrest that he did not believe a curfew was necessary for the team but that players needed to carry themselves responsibly.
England now find themselves bracing to go down 1-0 and with a huge cloud of controversy hanging over one of their most important players.
According to reports, Bairstow "headbutted" Australian's Cameron Bancroft at a bar in Perth earlier in November. I'm all for it. "There's a line, we'll headbutt the line but we won't go over it", Lyon said.
The ECB are yet to comment on the allegations.
However, England are now facing a full-blown disciplinary crisis.
Moeen Ali and wicketkeeper-batsman Jonny Bairstow tried to stem the rot with a 42-run sixth wicket stand after overnight batters Stoneman and Root (45-run partnership for the third wicket) failed to get going.