Associate Immigration Minister Craig Foss' office received the application in late August.
Bouwer, who is serving a life sentence for murdering his wife, Annette, in 2000 by administering a lethal cocktail of drugs intended to mimic the symptoms of a rare tumour, was made the subject of a deportation order in 2002. The order will mean he is returned to his native South Africa once paroled from prison.
Bouwer is seeking to have the order cancelled on compassionate grounds, owing to health issues.
A spokeswoman for Mr Foss said a decision on the application was expected by the end of the year.
The minister was seeking further information on the case from Immigration New Zealand at present, she said.
Bouwer's lawyer, David More, said he had ``heard nothing'' in regards to the application. He was not able to disclose details on Bouwer's health.
At a New Zealand Parole Board hearing in August, Bouwer asked for parole to be declined because of his health concerns.
The board heard Bouwer spent time in hospital,
but the details and extent of the illness have not been disclosed. However, the board's decision revealed it had resulted in periods of him being hospitalised.
He will appear before the parole board again next September.
Following his wife's death in 2000, Bouwer travelled to South Africa and returned bald and without his trademark beard. He told people the changes were a result of chemotherapy he had for prostate cancer. It emerged that story was false.