"Immigration agents would have power to enter the church," he said. "It's about how they feel."
But Unite Union organiser Joe Carolan, who is negotiating with a church, said the church had a record of supporting immigrants dating back to the dawn raids on Pacific Island homes in the 1970s.
For added symbolism, he plans a Māori welcome for the group, possibly on Monday (Waitangi Day).
"We are going to have some Maori leaders welcome them as tauiwi [newcomers]," he said.
The students are among almost 400 whose education agents in the Indian city of Hyderabad submitted fraudulent bank loan approval documents to prove that the students could afford to pay their fees.
The loophole they used has now been closed, and the students say they did not know what their agents did. Manoj Narra, 27, said he would have gone to a different agent if he had known that his agent was cheating the system.
"If I know, why should I go to that particular agent, because I have my family ready to pay everything?" he said.
He said his family paid more than $20,000 in fees for his business information systems course at UUNZ, a company owned by Remuera couple Jimmy Chen and Catherine Zhang and which offers courses in association with the University of Southern Queensland.
All up, including living costs, he has spent about $35,000 since arriving in Auckland in November 2015.
"I don't want to waste my father's money in this way," he said.
"I need justice. If I go back to India, literally I was not able to do anything about my future. My future is going to be dark if I want to go for any job or to any other country because I'm in the status of deportation."
Woodhouse's spokeswoman said the students' appeals were delegated to Immigration NZ officials because new Associate Immigration Minister David Bennett's authority to handle appeals is still passing through Cabinet.
Carolan said Catholic Church leaders had written to Prime Minister Bill English in a last-ditch appeal for clemency for the students.
"Bill English has a chance to put his hand up, to intervene in it," Carolan said. "He says he's a devout Catholic."