The Minister for Transport says he favours "some mechanism" to allow insurers to access information on penalty-points offenders.
However, he said, such information should be provided only if it led to reduced premiums for law-abiding drivers.
Announcing details of the scheme yesterday, Mr Brennan said endorsement information would initially be held by the National Driver File, a computerised database scheduled to come on stream next year.
He favoured the idea of people with better driving records enjoying lower premiums. However, there were legal issues around the disclosure of NDF details to insurers, as well as concerns that it would merely add to the general cost of premiums.
The Irish Insurance Federation said it was "encouraged" that the Minister was considering making the information available in some format.
However, it stressed that, regardless of the Minister's decision on the matter, policy-holders themselves had an obligation to disclose all road traffic convictions to insurers, including those under the new penalty points system.
The IIF chief executive, Mr Michael Kemp, said: "In order for insurers to set a fair motor insurance premium they need to be in a position to adequately assess the risk. Insurance policies are contracts of 'utmost good faith', and non-disclosure of material information simply increases premium costs for other policy-holders."
Welcoming the introduction of the first phase of the penalty points system, which covers speeding alone, Mr Kemp said the IIF "would like to see the further 61 offences that will incur penalty points come on stream as soon as possible, especially those that relate to driving without insurance, seat-belt wearing and careless driving."
