Michelle O'Neill told the BBC she still intends to publish the plan later this month, with an indicative budget.
On Thursday, Mrs O'Neill said there was "no longer an executive in place to agree a budget for an elective-care plan".
But she had talks on Friday with the finance minister about the funding.
The Stormont institutions face collapse following the resignation of Martin McGuinness as deputy first minister.
On Friday, the health minister said she "remains committed" to publishing the strategy to tackle waiting lists which she said were "totally unacceptable" to her.
She added that the amount of money needed was "sizeable" and that she was still in conversations with Mairtin O'Muilleoir looking at all the issues involved.
While the health minister says she will push ahead with publishing the plan, as there is no budget or executive in place, its implementation will be more difficult.

Her death certificate said in January that the 60-year-old, best known for her role as Princess Leia, had suffered a cardiac arrest.
But in a statement the LA coroner said the exact cause was unknown.
Sleep apnoea is a common condition in which a person stops breathing during sleep, either for a few seconds or minutes.
As well as listing sleep apnoea as a cause of death, the coroner's statement cited other factors, including heart disease and drug use.
In a statement released to People magazine after the coroner's ruling, Fisher's daughter Lourd said: "My mom battled drug addiction and mental illness her entire life. She ultimately died of it.
"She was purposefully open in all of her work about the social stigmas surrounding these diseases."
Her manner of death would be listed as undetermined, the coroner's statement said.
Fisher had been on tour promoting her book The Princess Diarist when she was taken ill on a flight from London to Los Angeles on 23 December.
She never regained consciousness and died on 27 December at the Ronald Reagan UCLA Medical Centre.
Her mother, actress Debbie Reynolds, died the following day.
The daughter of singer Eddie Fisher and Debbie Reynolds, Carrie Fisher made her film debut opposite Warren Beatty in 1975's Shampoo.
She also appeared in The Blues Brothers, When Harry Met Sally and Hannah and Her Sisters, and provided the voice of Peter Griffin's boss Angela in the adult animated sitcom Family Guy.
But her enduring fame is thanks to her role as Princess Leia in the original Star Wars trilogy. She will appear in the latest Star Wars sequel, The Last Jedi, which is to be released in December.

Jonathan Tran, 26, was in the grounds for more than 16 minutes before he was detained, it said.
He now faces a maximum sentence of 10 years in prison.
In a statement, the Secret Service said it was "extremely disappointed and angry" about the events of 10 March.
Mr Tran did not gain entry to the White House, where President Donald Trump was staying at the time.
However, Congressman Jason Chaffetz - whose House Oversight Committee oversees the Secret Service - claimed the intruder had managed to rattle a door-handle at the South Portico entrance.
According to court documents, Mr Tran told federal agents that he was a friend of the president and had an appointment.
He was carrying two cans of mace, a US passport, a computer and one of Mr Trump's books, authorities said.
The president praised the Secret Service for doing a "fantastic job" in apprehending the intruder.
Mr Tran had managed to climb a 5ft (1.5m) fence near the US Treasury Department, which is next to the White House. He then scaled an 8ft vehicle gate, and a shorter fence near the east wing of the White House grounds.
CNN reports that he set off several alarms after jumping the fence, but was able to avoid other sensors.
Mr Tran, who comes from Milpitas, California, had reportedly been spotted "looming around" Washington's Pennsylvania Avenue, where the White House stands, nearly six hours before his arrest.
The Secret Service said it had taken immediate steps to avoid further security lapses, and that over 50 people had been interviewed about the incident.
The intrusion was the latest in a series of breaches at the White House in recent years.
Security has been enhanced. In 2015, sharp spikes were installed on top of the black iron fence that circles the property.
The health minister has given further clarification around the publication of a new strategy to tackle hospital waiting times in Northern Ireland.
[NEXT_CONCEPT]
Star Wars actress Carrie Fisher died from sleep apnoea and "other factors", the Los Angeles County coroner says.
[NEXT_CONCEPT]
The US Secret Service has released new details of last week's White House fence-jumping incident, in which an intruder was discovered just steps from the main building.