The claims related to a contract between Metro North and a procurement company which allegedly included incentives to hire Stamp's daughter, a graphic designer, the Courier Mail reported.
In a statement the CCC said the arrest warrant would be activated if Stamp ever returned to Australia.
Stamp received a CBE for his services to healthcare in 2002 and had 18 years experience as a chief executive in the British National Health Service when he came to New Zealand in 2006.
At the time his daughter worked as a graphic designer at Waikato Business Publications.
Metro North's former director of corporate services Scott McMullen, 47, has also been charged and appeared in the Brisbane Magistrates Court on March 20, the Courier Mail said.
He faces three charges including receipt or solicitation of a secret commission and two counts relating to the alleged fraudulent creation of records.
Daniel Williams, 41, a Brisbane businessman, was arrested by the CCC on February 22 in relation to the same investigation.
He appeared in the Brisbane Magistrates Court in early March charged with offering a gift or secret commission and two other charges involving the alleged fraudulent creation of records.
Williams previously worked as Healthcare Procurement Partners managing director, which was allegedly provided with incentives to hire Katy Stamp through the variation of an existing contract with Metro North, the Courier Mail said.
No allegation of misconduct has been made against Katy Stamp, who according to her LinkedIn profile is now freelancing in London.
The CCC said it would allege the three men were involved in "providing or receiving a secret commission after arranging employment for a family member of the then senior Queensland hospital and health service employee".
"It is further alleged this occurred by varying an existing contract between the hospital and health service and a company associated with the 41-year-old man," the CCC said.
Metro North Hospital and Health Service said in a statement in March: "We have worked closely with the Crime and Corruption Commission throughout their investigation and as the matter is before the courts we are unable to comment further".