Five Kildare routes are among the bus routes which could be privatised.
The government plans to open 10 per cent of public bus routes to market, including 23 Dublin Bus routes and five Bus Eireann routes.
There's been opposition from unions representing transport workers, which have warned of industrial action if privatisation goes ahead.
Talks between the National Bus and Rail Union, Siptu, the National Transport Authority and management from both companies are ongoing at the Labour Relations Commission.
The next round of negotiations are set for Monday.
The five Bus Éireann routes are commuter services, primarily from Kildare to Dublin city centre.
Four of the routes serve Naas, with one of the buses extending to Athy and another to Portlaoise.
The fifth service is the Edenderry to Dublin route, which serves several parts of Kildare including Clane, Prosperous and Allenwood.
However consumer network One Big Switch is welcoming the announcement that private operators can bid on the routes.
It's as they claim fares have increased by 23% on the main Dublin to Naas route currently operated by Bus Éireann.
The resulting fare increase means the average commuter is paying 570 euro a year more to commute with Bus Éireann than 4 years ago, according to One Big Switch.