A meeting of the board of Console is continuing this evening in Dublin to discuss the future of the charity.
A recommendation to wind up the charity has been put to the board by the interim CEO, David Hall and is expected to be accepted due to the serious financial position the organisation is in.
It is understood that the board may reconvene tomorrow to conclude the issue.
If the proposal to wind up Console is agreed, the organisation will then go to the High Court to seek approval for the move.
In tandem with the meeting this evening, talks are also continuing separately with the HSE on another agency taking over the Console services.
The organisation has been in crisis since the revelations on expenditure in the RTÉ Investigations Unit report on 23 June.
Meanwhile, HSE Director General Tony O'Brien has said contingency plans have been put in place should Console decide it cannot continue to operate.
Mr O'Brien said the Health Service Executive continues to fund the suicide bereavement charity, on an arrears basis, in order to ensure that those in need are not left without vital services.
He added that the HSE's primary concern is to maintain the essential services that it funds.
Speaking on RTÉ's Today with Sean O'Rourke, Mr O'Brien said: "The directors of Console and its interim CEO obviously are faced with a difficult decision about whether that organisation is financially sustainable.
"What we have done, we have continued to fund on an arrears basis even up to this week, to sustain the important helplines and counselling services for people who are bereaved by suicide.
"And we have contingency plans, such that, if Console decides it can no longer trade ... we will put in place replacement services."
Mr O'Brien said that at no time did the HSE fund more than 43% of the monies Console had in total and it was purchasing services from Console that were paid for in arrears.
He added that the HSE was happy the funding given to Console was of high value to the clients availing of them and Console's interim chief executive has said the executive was probably not paying enough for the services provided.
However, he said the HSE does not have regulatory powers over charities.
The executive has provided the charity with around €20,000 in funding to cover services provided so far this month.
The charity has 60 counsellors employed, with over 300 people still in active counselling.
Yesterday, High Court proceedings against the founders of the charity were adjourned for a week.
The court heard that more time was needed to consider three sworn statements which had been submitted by former chief executive Mr Kelly, his wife Patricia and their son Tim.
Lawyers for Mr Hall said that both sides also needed time to agree living expenses for the Kellys, as injunctions freezing assets and bank accounts remain in place.
Mr Justice Paul Gilligan said any motion about living expenses could be brought to court in the next week if necessary, before adjourning the case to Tuesday.
The HSE will appear before the Public Accounts Committee on Friday to answer questions on its dealings with the charity.
