The Herald on Sunday understands the total amount the students handed to the Auckland-based agent was about $250,000.
Jessica Phuang, police Asian liaison officer, met the two students who are in Auckland this week and said the matter was being treated as a "priority".
"Police advise international students never to share their bank account details and PIN numbers with anyone, and they should always keep hold of their passport and only give a copy out if they have to," Phuang said.
Detective Inspector Scott Beard advised students to always confirm with an educational institution that the people they were dealing with were approved agents.
The 11 were to have been enrolled for courses at three private training establishments - NSIA, Edenz College and UUNZ Institute of Business.
One of the alleged victims, Nawon Lee, 25, said she met the agent online in 2014 through an introduction from a former NSIA student.
"From the start she kept asking me to transfer money into her account but I didn't do it because I didn't know her then," she said.
Lee came to Auckland on a working holiday visa last year and met the agent for the first time at a McDonald's restaurant on Queen St.
"I told her my dream is to be a chef, so she told me all about NSIA and offered to give me a tour of the school," she said.
She claimed she handed the agent her Korean bank card to access funds from her Korean bank account after she was told it was easier than transferring money to New Zealand.
Lee was given a receipt for $19,990 from NSIA for her diploma in culinary arts course - but the school said the receipt was fake.
She claims the agent took about $36,000 from her account because she needed to show proof to Immigration New Zealand that there were enough funds for living expenses.
Another alleged victim Jungchul Chae, 34, said he handed about $17,000 to the agent to enrol him for a business management course at UUNZ.
Chae was introduced to the agent while holidaying in New Zealand last year.
"I feel stupid and totally regret that I put my trust in her," Chae said.
Lee and Chae sought help from the Korean Consulate in Auckland and also lodged a police report.
The agent is believed to have left New Zealand, and could not be reached for comment.
A local Korean woman, who is assisting the students, said nine others had lodged a report to police in Korea.
"Some had already bought tickets to come to New Zealand and are shocked that this has happened," she said.
"They cannot come now because they have no school, and that means they cannot get a visa."
A visit to the agent's rented Auckland home found it abandoned.
The property manager retrieved some property belonging to students including one Korean passport, the woman said.
Rebecca Kim, senior adviser at the Consulate of Korea, said the consulate had been providing support.
Edenz College chief executive Rob Simpson said the school was deeply concerned.
"We are actively trying to assist students who have contacted us," he said.
"Unfortunately we have no control over the operations of fraudulent agents so have referred these matters immediately to the authorities who, we believe, are investigating."
Simpson said Edenz had cancelled its agreement with the agent last year.
Rod Marvin, chief executive of Intueri Education, the parent company of NSIA, said that the agent concerned was not one of the institute's current approved agents.
UUNZ marketing manager Shingyi Kim said the college had enrolled students through the agent in the past, but this was the first time such an issue had surfaced.
The New Zealand Association for Migration and Investment said tighter Government controls were needed on education agents.
"Education agents are, in most cases, working for their own self-interests and not those of the student," said association chair June Ranson.
"It currently appears that a stringent framework for recruiting and monitoring of the education agents is not being practised by many of the education institutions."
Last month, the Herald reported that several schools with thousands of international students had been called in by NZQA and Immigration New Zealand for a warning meeting over unrelated student visa fraud.
