The former chief of staff to ex-NAB boss Andrew Thorburn has been arrested over a $40 million fraud against the bank.

Rosemary Rogers, 43, was arrested by detectives on Tuesday at Sydney Police Centre in Surry Hills.

"The woman, who is a former executive employee of the financial institution, will be charged later today," NSW Police said in a statement.

The news comes after Human Group director Helen Rosamond, 43, was charged last week with 56 bribery offences, one count of obtaining benefit by deception and one count of attempting fraud.

Rosamond allegedly forked out more than $6.6 million in bribes to maintain a relationship between her training company and NAB.

Acting Assistant Commissioner Stuart Smith on Friday said the "corporate corruption" involved "senior executives".

He said at the time he wouldn't rule out further charges being laid.

The total amount involved in the alleged fraud is some $40 million. The criminal behaviour occurred between 2013 and 2017, Mr Smith said.

The relationship between Human Group and NAB dates back 12 years with contracts worth $118 million.

A NAB spokesperson on Friday said the alleged fraud was first reported by a whistleblower.

"NAB responded immediately, investigated and reported it to police," the spokesperson said in a statement.

"If the alleged fraud is proven, it represents a most serious breach of trust by a former employee."

The bank stressed that "NAB is the victim in this matter".

"Police have confirmed that no one at NAB is under investigation, including former CEO Andrew Thorburn, and there is no suggestion of any wrongdoing by anyone at NAB."