Bairstow and Bancroft crossed paths shortly after England arrived in Australia, where they started their tour with a tune-up at the WACA.
Jonny Bairstow is an England cricket star who represents his country in Test, One-Day and Twenty20 versions of the game.
Prior also opined that what Bairstow is accused of doing is nothing like David Warner' infamous run-in with Joe Root in 2013. England are already in the soup after their mainstay all-rounder Ben Stokes is still under police investigation after being involved in a fight0night outside a Bristol nightclub.
"I understand from the camp that Bairstow and Bancroft were having a drink together", Agnew told the BBC.
The comments, which centred around the pair telling Bairstow "we know what you did to our mate in Perth" might have contributed towards a careless stroke from one of England's best batsmen as they crashed to near defeat.
The England Cricket Board are investigating the incident that allegedly occured over three weeks ago at a Perth pub while the English team touched down for a tour match against the Western Australian XI.
Big Brother 2.0? FDA Approves World's First Electronic "Smart Pill"
The ingestible sensor is activated by gastric juices and sends a unique, identifying signal to a wearable patch. Patients can allow caregivers and physicians to access the information through an online portal.
They had arrived in Australia with questions having been raised, including by ex-England opener Michael Vaughan, about their team culture following the barrage of punches thrown by Stokes in the hours after a one-day global against the West Indies in September.
Following the reports, the European Central Bank issued a statement, saying: "At close of play in Brisbane today, we were made aware of allegations of an incident in Perth four weeks ago".
Seamer Mitchell Starc, meanwhile, has confirmed that Australia would continue to target the fragility of England's tail as his side moved to the brink of a 1-0 lead in the five-match series on Sunday.
'There has been no report of any incident from the venue, security or police and there was no injury reported, ' said the European Central Bank statement. "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", ECB spokesman said in a statement.
Last month Bairstow was one of three England players fined by the European Central Bank for "unprofessional conduct".