The director general of FAS, Dr John Lynch, is believed to be the favourite to replace Mr Brian Joyce as chairman of CIE.
Mr Joyce resigned two weeks ago, citing "fundamentally differing views" from the Minister for Public Enterprise, Ms O'Rourke, over the autonomy of the State-owned transport group. Ms O'Rourke denied inappropriate interference in the management of CIE.
The Minister's spokesman said a replacement for Mr Joyce would not be appointed until next week. He declined to speculate on the candidates for the position.
It is thought unlikely, however, that a former managing director of the Industrial Development Authority, Mr Padraic White, will be asked to take the role.
Attempts last night to contact Dr Lynch failed. A former chief executive of Bord Gais Eireann, Dr Lynch has been with FAS since 1990. He is regarded as having a strong grasp of industrial relations issues and believed to have refocused the State training agency towards a more customer-friendly service.
But Ms O'Rourke may encounter difficulty persuading a candidate to take the chairmanship of CIE, which in recent years has been regarded as something of a "poisoned chalice".
This is especially so given the controversial departure of Mr Joyce. The former chairman accused Ms O'Rourke of failing to grant the transport firm autonomy in the management of its industrial relations and fare structures.
Mr Joyce also criticised the Minister for the failure to grant public service contracts to CIE, through which the group would be subsidised for providing bus and train services on unprofitable routes. It later emerged that the Attorney-General had advised against the creation of such contracts.
Difficulty surrounds the management of the CIE companies. The industrial relations climate is not good and it is unclear how long the group itself will continue to manage Iarnrod Eireann, Bus Eireann and Dublin Bus.
Ms O'Rourke has said she favours establishing the three companies independently of CIE. Under this proposal, the group would cease to exist in its current form and retain responsibility only for workers' pensions and related matters.
The new chairman will also have overall responsibility for the implementation of the State's investment of more than £2 billion in public transport under the National Development Plan.
One observer suggested that Mr Lynch's grasp of industrial relations questions would be a strong point in his favour should he be offered the position.
Like CIE, FAS is seen as a complex organisation with strong trade union representation on its board. Mr Lynch is said to have a consensual management style with a heavy emphasis on business strategy and a good relationship with the trade union movement.
Establishing a good relationship with Ms O'Rourke will be a primary task for Mr Joyce's replacement, as the Minister and CIE's group chief executive, Mr Michael McDonnell, are not close.