Doubts are growing about the feasibility of plans by the Minister for Arts, Sports and Tourism, Mr O'Donghue, to engage the private sector in refurbishing the Abbey Theatre in Dublin.
Members of the Abbey council have also voiced concern at the plan.
A spokesman for the Minister has confirmed he is to seek Government approval for a public-private partnership scheme to refurbish the national theatre. The tight financial situation, he said, meant the Government could not fully fund the refurbishment project.
"I would like to see the advancement of the rebuilding of a new national theatre, probably on the site of the Abbey," the Minister said, adding that a mechanism would be formulated so private investors would recoup their investment.
However, a number of companies often associated with such sponsorship projects said they would not consider investing.
Mr Jim Kelly, AIB, said the bank "wouldn't rule it out, but to be honest we are totally focused on the projects we already have".
Ms Anne Matthews, Bank of Ireland, said the bank already had "a lot on with the Special Olympics and the Millennium Scholars programme".
A spokeswoman for Aer Lingus said there was "no way" the company would consider investing in refurbishing the Abbey.
"We have pulled out of almost all our sponsorship projects due to the current financial situation."
A number of council members at the Abbey expressed concern at Mr O'Donoghue's plan.
Mr Fergus Linehan, director of the Dublin Theatre Festival, said it would be "terrible" if the plan entailed any reduction in the Government commitment to the national theatre.
"This is not a vanity project. The refurbishment just has to be done. We have to have a national theatre and the building it now has is in dreadful disrepair."
Another council member, Mr Des Geraghty, said it would be important that whatever private investment there was came "with no strings attached".