It is expected a memo will be brought to Cabinet early next week to approve the plan to provide significant emergency funding to the charity, which is in the midst of a major financial crisis.
The charity, one of the largest providers of homeless services in the country, is believed to require State funding by the first week of December to keep running its services.
The trust has been on the brink of collapse since the middle of the year, due to significant debts and a shortfall in income.
Department of Housing officials have been considering a request from the charity for a bailout for more than a month.
A memo is currently being finalised, which Mr O’Brien is preparing to bring to Cabinet on Tuesday, sources said.
Under the proposal, the department would provide a bailout €15 million to the charity, with funding to be released on a phased basis between now and March 2024.
The charity will have to prepare a detailed plan by the end of February setting out “how it will put itself back on a sustainable footing”, one department source said.
The funding will also be tied to commitments that the charity improves basic budgetary and financial practices, which had been found to be subpar, the source said.
Initially it was expected the level of funding needed might be in the region of €8 million. That estimate was later revised upwards significantly.
Earlier this month, the Dublin Region Homeless Executive (DRHE), which funds homeless services, released some interim emergency funding to the organisation, following warnings it would need €2 million to continue to stay afloat in the short-term.
The charity reported €60 million in income last year, some €43 million of which came from public funding, with the majority of the remainder made up from donations.
The trust owes trade creditors around €7 million and recently said it has had to review its plans to deliver 500 homes over the next three years, due to current financial troubles.
Several creditors owed money by the charity have issued solicitors’ letters seeking payments, while some suppliers previously threatened to stop providing services unless unpaid bills were settled.
It has also been exploring selling several properties currently used for homeless accommodation to raise several million euros, as well as examining if it could secure a bank loan.
The trust is facing two parallel statutory investigations, by the Charities Regulator and the Approved Housing Bodies Regulatory Authority, into financial and governance concerns.
Francis Doherty, who took over as chief executive at the start of June, resigned in early October, claiming tensions with the board made his position untenable.
In a resignation letter, Mr Doherty said he had identified a “substantial amount of concerning information” about practices that predated his appointment.
He claimed this included the “potential mismanagement” of donations, “huge” spending on a homeless hostel in Co Kildare, potential conflicts of interests and how the charity’s accounts “overstated” the value of its assets.
Daniel McLoughlin, the former head of South Dublin County Council, was brought in last month as an effective interim chief executive.