The Irish Insurance Compensation Fund may have to cover outstanding claims following the collapse of a Danish registered insurance company.
Qudos went into liquidation late last month, and the company has around 50,000 customers in Ireland.
Payouts on claims have been put on hold.
Finance Minister Pascal Donohoe says it is estimated there could be around 1,400 claims outstanding for Irish policyholders.
The figures are contained in a written parliamentary response to Fianna Fáil's Finance Spokesperson Michael McGrath.
A change in Danish law earlier this year could mean that the claims will have to be paid out in Ireland.
Minister Donohoe noted that the Danish Finance Ministry has indicated that claims will be met if the company remains in 'solvent liquidation'.
However, he added: "The Ministry also indicated that if ultimately Qudos is placed into bankruptcy, and this happens after 1 January 2019, that the Danish Insurance Guarantee Scheme will not be liable to meet these claims due to a legislative change in May 2018.
"In such a situation claimants may instead be eligible for cover from the Irish Insurance Compensation Fund (ICF), subject to its terms and conditions and the particular circumstances of the case."
He stressed that the situation will become clearer with the next two weeks, after liquidators finish their review of Qudos.
The ICF allows payments to policyholders here when an insurer authorised in another EU member state goes into liquidation.
The Central Bank has already recommenced that customers affected by the Qudos liquidation should contact their insurance broker to arrange alternative insurance cover.