Some 480 retail outlets nationwide are being sought to participate in the scheme by the Courts Service.
It is estimated that retailers will accept as many as 93,000 fine payments per year.
Last year, the Courts Service collected over €13.75m in fines with a 76% collection rate.
Fines for motoring offences accounted for nearly half or €6.8m.
Every court venue will have five separate outlets to accept payments under the plan.
In Dublin, the Courts Service is demanding that the firm providing the service will have 55 retailers in place to accept payments.
Cork is to have 50 retailers, with Galway to have 40. Other counties to have in excess of 30 retailers to accept the payments include Tipperary, Kerry, Mayo, and Donegal.
Counties with only one court venue such as Carlow, Kilkenny, Laois, Longford, and Offaly will require only five retailers.
Earlier this year, the Government enacted the Fines (Payment and Recovery) Act 2014 and the Courts Service has now advertised for firms to carry out a large proportion of the administration.
In its documentation, the Courts Service is estimating that the payment online of fines will account for 32% of 65,000 payments annually, with 15% or 30,500 to be paid by post, and 7% or 14,000 to be paid over the telephone.
Firms tendering for the work are being asked to base their price on set-up costs, infrastructure, resources for a low-call phone line; transactional costs, and discounts.
The Courts Service is also seeking a firm to carry out the printing and posting of almost 500,000 separate documents per annum in a separate tender under the new fines system.
One of the objectives of the new legislation is to reduce the number of people sent to prison each year and to allow people to pay in instalments.
According to the Courts Service, the new legislation aims to significantly reduce the involvement of the gardaí in the fines process.
However, it will result in additional work for the Courts Service.
Firms have until October 15 to lodge tenders.