A department spokes-woman told the Herald that Xue could lose some of his inmate privileges if investigations found the offences to be internal, or hauled back to court if they were deemed to be more serious.
A Chinese Herald reporter, Conney Zhang, interviewed Xue in prison in 2009, despite Corrections saying that it had not approved any media interview requests, including those from the Chinese Herald.
It was during the interview with Ms Zhang that Xue first said he would be writing a book "so people can know the truth".
Jeanette Burns, Corrections general manager prison services, said the existence of such a book was "highly inappropriate" and would "likely have a significant negative effect on his victims in the community".
"We have not given permission to the offender to publish a book and therefore we believe there may be a breach of Corrections Regulations governing contact with prisoners," she said.
Ms Burns said it was an offence under the Corrections Regulations for a journalist to interview a prisoner for the purpose of obtaining information and publishing it without the approval of the department's chief executive.
"We take unauthorised correspondence with prisoners seriously and are investigating the situation," she said.
The department said there was no indication that Xue was receiving an income from the book or newspaper articles.
Maggie Chen, Chinese Herald chief executive, defended the publication of the book and said it had been done with the department's knowledge.
She had a 2010 letter from Corrections general manager Mike Martelli that said: "Because the material you have was produced solely by prisoner Xue and not the result of an interview, the Corrections Regulations do not prohibit publication."
The same letter also said: "However ... it must not suggest or imply that it was done with departmental approval."
Ms Chen said she believed her reporter, too, would have had clearance from the department for the 2009 interview.
Xue was caught in the United States after five months on the run and brought to New Zealand where he was convicted and sentenced to life imprisonment.
From the book
"The whole world has accused me of being a murderer, but I dare not even kill a chicken, not to mention kill my wife."
Xue said in his book three people could have killed his wife - a woman business associate, a neighbour or his wife's lover.
He said he fled New Zealand because he owed $20,000 in business debt and was unaware his wife was dead, but left their daughter at the Melbourne rail station, where she could be easily found by security, as a revenge on his unfaithful wife.
"A middle-aged fat woman witness, who was my temporary sex partner when my wife was away, gave false evidence in Court. The prosecutor asked if she saw me bring an axe to Wellington, and she said yes. The landlord and tenants at the Wellington house where An An stayed never saw me with an axe.
"She claimed I told her over lunch that I was going to kill An An. If I was going to kill her, I would never reveal it in that way. The judge is a fool to believe the woman."
