Section 501 is the same section of the Act used to deport hundreds of New Zealanders with criminal convictions on character grounds.
National's immigration spokesman and former immigration minister Michael Woodhouse this week called for Manning to be banned from New Zealand because of her criminal record.
Manning, a former US Army intelligence analyst, served seven of a 35-year prison sentence for theft and espionage after releasing hundreds of thousands of classified or sensitive documents to Wikileaks. Her sentence was commuted by former US President Barack Obama.
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," he said on Tuesday.
Immigration New Zealand has confirmed it has received a request for a special direction from Manning's representatives.
Manning will need a special direction as she is subject to character provisions in section 15 of the Immigration Act. If that request is declined she can go to the Immigration Minister or his associate for reconsideration.
Woodhouse said Manning would not meet the criteria for a special direction but Jamil said she was confident of a positive response from Immigration New Zealand and the Government.
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.
The Free Speech Coalition, which was set up after calls to ban controversial Canadian speakers Lauren Southern and Stefan Molyneux from New Zealand, has said it is the right of New Zealanders to hear from someone who is noteworthy, albeit controversial.