James O'Brien said he does not have powers to direct and fund any one union into a more viable entity, so winding-up a union is the only option available at present.
He also revealed, at the Economic Regulatory Affairs Committee, that some credit unions have had to give a lot of their members more time to repay loans.
Mr O'Brien said there had been significant amounts of what are termed 'rescheduled loans' in recent years.
As a result, new rules are being imposed on all credit unions to put aside more money in case more loans are not repaid.
He said the stresses caused by loans not being repaid on time had increased quite dramatically.
Mr O'Brien said individual credit unions will have to put aside 10% of the value of all loans.
At present, 85% of credit unions have put aside 7.5%, while a significant number have already achieved the 10% level.
Mr O'Brien said these preventative measures, of building up credit union reserves in case more loans are not repaid, were to ensure they did not go the way of the banks.
He also told the committee that arrears on loan repayments to credit unions had doubled in the last couple of years.
Jonathan McMahon from the Central Bank told the committee there are 20 credit unions with serious solvency issues.
Mr McMahon said it was likely that there were serious problems in the credit union sector.
