The ANZ Bank says it is "completely shocked" by a police investigation into an alleged drug trafficking network operating out of its Melbourne offices.

Australian Federal Police have launched a probe into the alleged narcotics syndicate running out of the bank’s debt collection department.

Fourteen staff who worked in the bank’s former city offices in Collins Street, and later when the department moved to Dorcas Street in South Melbourne, have reportedly been linked to the alleged syndicate.

ANZ spokesman Stephen Ries said a number of staff linked to the investigation had left the bank "some time ago", but he would not elaborate on why they had left, or if they had been sacked.

"We have been completely shocked by this matter and everyone at ANZ is incredibly disappointed at the matters the police are looking into," he said.