The administrator running Quinn Insurance says he hopes most of the 900 cuts announced at the company will be achieved through voluntary redundancy.
Staff were told on Friday that the jobs, including 200 posts in Enniskillen and Derrylin, must go to ensure the future of the business.
Michael McAteer from Grant Thornton says a trawl for volunteers will start almost immediately.
The company is now officially up for sale.
Mr McAteer said he is hopeful that the initial redundancies for almost 350 staff, will be reached voluntarily.
"We have asked people to come forward by May 19th, indicating whether they would be willing to take the voluntary package. The process is over a 12-15 month period, so time will help in that regard.
"Employee representative committees, which have been established in each of the locations will be sitting down with staff and consulting with them and explaining the process to them in more detail and that's when we'll be looking for volunteers to come forward."
The company's owner Sean Quinn has said he and his family are "devastated" by the redundancies.
The job losses are larger than predicted. It was thought that 800 jobs would go.
179 jobs will go in Enniskillen and 21 in Derrylin.
On Friday, the board of Quinn Group said Quinn Insurance should be sold.
It said it would be "best protected" under new ownership.
Administrators said the massive cuts - hitting more than a third of the company's 2,400-strong workforce - were needed to safeguard the business's future.
In a statement, Mr Quinn said he wished to express his appreciation for the "huge effort" of staff.
He added: "I would also like to personally thank all the staff and the very loyal customer base who have shown their overwhelming support as well as the thousands of people across the country who have shown their support in various ways.
"At the group board meeting this week we decided that given the developing situation it was in the best interest of Quinn Insurance that we would offer it for sale so as to protect the business and maintain the maximum number of jobs within it.
"I just hope that in time the company will return to the dynamic business it was up until 30 March and that employment levels will increase again in the future. Our thoughts are with all of the staff today."
About 700 jobs will go at the company's offices in Cavan, Navan, Dublin and Manchester.
The firm's problems stem from massive losses made by Sean Quinn in a stockmarket gamble on the now-failed Anglo Irish Bank.
Although the job losses will be mostly in the Republic, the restructuring relates primarily to Quinn Insurance Ltd's businesses in the UK.
Just over half of Quinn's 1.3m customers are based in the UK and much of that business is handled by staff at Quinn's offices in the Irish Republic.