More than 900 workers at Quinn Insurance have applied for voluntary redundancy, but others who did not put themselves forward could still be at risk of losing their jobs.
The insurance company's administrators said in a statement that they would decide over the next two weeks whether those who had expressed an interest in voluntary redundancy would qualify on a "site by site, role by role" basis .
"Quinn Insurance Ltd confirms the number of voluntary redundancy applications exceeds the number of targeted head-count reductions.
"It is hopeful therefore that the voluntary-led process will mitigate a need for compulsory redundancies," the statement said.
"The administrators have previously set a target number of head-count reductions by location and by grade. Once the analysis has been completed, it is the company's intention to brief the employee representative committees and our staff of the findings prior to any announcement to the media."
While they did not give a breakdown, it is understood that a portion of they applications are from Quinn's operations in Northern Ireland.
Quinn Insurance was forced into administration on March 30 after the Irish financial regulator Matthew Elderfield became concerned it was not holding enough reserves to cover its liabilities.
He stopped the company writing new business in the UK for several weeks.
Administrators Grant Thornton announced earlier this month that 900 jobs were to be axed in order to save the company, including 200 in Enniskillen and Derrylin. They said the restructuring was necessary to cut close to £30m off the annual wage bill and put the company back on a firm financial footing.
The job cuts will be carried out over a 15-month period through to the middle of next year.
More than 40 parties have expressed an interest in buying Quinn Insurance since it was placed into administration, including US insurance giant Liberty Mutual.
Interested parties had been expecting a detailed information memorandum on the firm by the end of the month, but it now looks like potential bidders may have to wait another two weeks for the administrators to untangle Quinn Health from the wider Quinn Group.