The Minister for Transport, Mr Brennan, will meet with union leaders at the Labour Relations Commission today in an attempt to reach agreement on the shape of public transport for the future.
Mr Liam Tobin, general secretary of the National Bus and Rail Union, said there was a "large gap" to be bridged between unions and the Minister for Transport, Mr Brennan.
However, he said a successful conclusion to what had been a protracted process was possible.
Unions have been in dispute with Mr Brennan for nearly two years over his plans to break up CIÉ and open up bus markets to increased competition.
It emerged in July, however, that a compromise deal was possible when the chairman of the current talks process, Mr Kevin Foley, said the objectives of both sides could be met.
The two sides meet today to begin three days of intensive discussions, chaired by Mr Foley, with a view to concluding an agreement by Friday.
Union sources were sceptical this week about the prospects for a deal in that timeframe, and Mr Tobin said yesterday the talks posed "a serious challenge" to everyone involved.