Manning was denied a visa to Canada last year but was granted a temporary permit in May this year for a series of public talks.
Woodhouse said if Manning's application had come across his desk as immigration minister he would have declined it.
"She was convicted of a crime for which she has absolutely no remorse and not only that, she intends to profit from it by selling tickets to meetings where she talks about exactly what she did. I don't think that's appropriate and I think the associate minister should be declining it."
Immigration New Zealand said it had received a request for a special direction from Manning's representatives.
"Ms Manning needs a special direction as she is subject to character provisions in section 15 of the Immigration Act 2009. An appropriately delegated INZ staff member will look at the representations in the first instance.
"If the request is not successful Ms Manning may choose to make representations to the Minister or Associate Minister of Immigration," a spokesperson said in a statement.
Woodhouse did not believe Manning would not meet the criteria for a special direction.
Suzi Jamil of Think Inc, which is bringing Manning to New Zealand, said she was confident of a positive response from Immigration New Zealand and the Government.
The Free Speech Coalition, which was set up after calls to ban controversial Canadian speakers Lauren Southern and Stefan Molyneux from New Zealand, said it was not an issue of defending breach of confidence or leaking military secrets.
"Rather, it is the right of New Zealanders to hear from someone who is noteworthy albeit controversial," spokesman Chris Trotter said.
"As a democracy, we have a right to be informed on the activities of our friends on the international stage. New Zealanders deserve a chance to hear her speak."
He gave examples of other convicted criminals allowed into New Zealand - including Nelson Mandela.
