Dún Laoghaire-Rathdown County Council is assessing responses from private-sector companies to an advertisement for a "parking enforcement and monitoring service" in south Dublin.
The council said, however, that clamping would only be introduced as a last resort.
The call for "expressions of interest in managing the parking facilities and enforcement of parking restrictions" was advertised recently on the council's website and a deadline of last Friday was given for submissions from suitable companies.
The council received about six requests for further details and at least four proposals were put forward.
While the request for a private-sector partner comes after years of parking difficulties in Dún Laoghaire town centre, the advertisement makes it plain that a system was required across the council's administrative area, which runs from Dún Laoghaire to Ballinteer and from near the Merrion Gates to the border with Co Wicklow.
The current scheme is enforced by wardens under the control of the Garda Commissioner. Where fines are imposed they benefit the Department of Justice, although the warden enforcement schemes generally do not make a profit.
Speaking to The Irish Times yesterday, the council's senior executive officer in charge of transportation, Mr John Guckian, stressed that "there are currently no proposals for clamping".
Mr Guckian said "what we do need is an adequate and properly run system".