Unions are set for a renewed stand-off with the Minister for Transport, Mr Brennan, over his plans to reform CIÉ.
Officials in his Department are to meet unions in the company on June 8th, but no further talks have been fixed for beyond that date.
Five days of intensive discussions this month failed to produce a breakthrough, and there is now considered to be little prospect of agreement.
If potential for progress cannot be identified at the June 8th meeting, industrial action will become increasingly likely.
Unions are opposed to plans by Mr Brennan to allow private operators to take control of 25 per cent of the Dublin bus market.
There is also no agreement on other reforms outlined by the Minister, including a plan to break up CIÉ and establish its subsidiaries, Bus Éireann, Dublin Bus and Irish Rail, as independent entities.
A joint position paper prepared by the unions after the sides last met on May 18th points to a continuing wide gap between the sides. It says unions require a guarantee that Dublin Bus will not be diminished in size as a result of the reforms.
However, the paper indicates that the parties have not yet been able to agree on a formula that defines the size of the company.
Unions argue that any measurement of the company's size must primarily take account of its route network, not the number of buses.
They insist any new arrangements should allow for Dublin Bus's continued growth "in line with natural growth in the market", an issue not adequately addressed by the Department's proposals, the paper says.
Mr Brennan is understood to favour a formula in which Dublin Bus would be restricted from expanding for a time, to allow private operators to gain a foothold in the market.
Some measure of agreement has been found on the Minister's plan to establish a regulator for the sector.
The unions say they support the transfer of regulatory responsibility from the Department to a new authority but they have significant concerns about the structure, remit, accountability and resources available to such an authority.
Both sides are understood to be pessimistic about the prospects of agreement.
