Mr Cushnahan served on Nama's NI advisory committee from 2010 to 2013.
On Friday, Nama reported him to police in the Republic Ireland as well as the UK National Crime Agency.
It follows a BBC Spotlight programme which broadcast a recording in which Mr Cushnahan took a Â£40,000 cash payment from a Nama client, John Miskelly.
According to what Mr Cushnahan says on the recording, which was made in 2012, he was going to help Mr Miskelly with a refinancing deal which would get his assets out of Nama.
Mr Cushnahan also claimed he could influence a senior Nama official, Ronnie Hanna.
There is no direct evidence of wrongdoing by Mr Hanna and he firmly denies that he had any improper dealings with Mr Cushnahan.
Mr Cushnahan has denied any wrongdoing and told the BBC he would not be providing any further responses because of the ongoing NCA investigation.
Mr Miskelly said "payments made by me to any persons have been lawful".
Nama, the National Assets Managaement Agency, was established by the Irish government in 2009 to take control of billions of euros of bad property loans which were damaging the Irish banks.
It sold its entire Northern Ireland portfolio to Cerberus, a US investment fund, in 2014.
The Republic's Comptroller and Auditor General (C&AG), is to publich a report on the deal later this week.
It is expected to say that failings in the sales process could have resulted in "hundred of millions of euros" not being realised.
This is the second complaint by Nama to the Standards in Public Office Commission about Mr Cushnahan.
The first related to a section of the Ethics in Public Office Act and whether Mr Cushnahan made all required disclosures while a member of the NI Advisory Committee of Nama.
Meanwhile, Sinn FÃ©in leader Gerry Adams has said Northern Ireland's First Minister Arlene Foster should reconsider her opposition to a cross-border inquiry into Nama.
Mrs Foster has said the National Crime Agency was the appropriate organisation to investigate.
Speaking on Tuesday, Mr Adams said her Democratic Unionist Party was involved in a whole series of cross-border co-operation.
"Arlene Foster should co-operate with the Irish government to bring forward the most thorough, robust, transparent investigation," he said.
Nama has lodged a new complaint about its former adviser Frank Cushnahan to the Republic of Ireland's Standards in Public Office Commission.