The clamping company, Control Plus, is facing competition for Dublin City Council's clamping contract which is coming up for renewal shortly.
Control Plus has held the contract since 1998, but is being challenged for it by two other companies which have submitted bids to the council.
The Control Plus contract, which is worth around €8 million a year, runs out on October 31st.
The council says it will announce, within the next two weeks, which company will handle clamping in the city for the next five to seven years.
An Irish car-parking company, Park Rite, and a French building conglomerate, Vinci, have both made the final selection stage along with Control Plus.
Vinci went head to head against Control Plus for the first contract in 1998 and is now making a second attempt to enter the Irish market.
Park Rite is the State's largest operator of public car-parks and is the only Irish company in the race.
This is the first time the clamping contract has come up for renewal. The first contract was due to end last year; however, because of errors in the tender document issued by the council, the existing company, Control Plus, was given an extension to the end of this month.
Choosing the clamping company is a function of the city manager, Mr John Fitzgerald. However, the Fine Gael group of city councillors has stated that it does not want the Control Plus contract renewed.
"Clamping is always going to be problematic, but we think there is a certain lack of investment in staff training in Control Plus," the Fine Gael group leader, Cllr Gerry Breen, said.
He added that he did not expect the contract would be awarded to Control Plus.
A former Labour lord mayor, Cllr Dermot Lacey, said he was unhappy with the way Control Plus had managed the service, but it was "a bit presumptuous" to call for its contract to be removed without a proper analysis of its service.
"There have been problems with Control Plus, and I do think they have been overzealous, but I want to see if these problems are resolvable, because there is nothing to say that any other company wouldn't be the exact same," he said.
Figures circulated earlier this week, indicating that an average of 2,300 complaints were made each year about Control Plus, were inaccurate, according to the company.
The figure represents the number of appeals against the €80 clamping fine, a spokeswoman for Control Plus said. The company clamps around 60,000 cars in the city each year, and complaints about the service or staff account for around 0.2 per cent to 0.5 per cent of these, she said.
Control Plus collected €4.1 million in revenue for the council last year and charged €8 million for the service.
