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.
The health minister has given further clarification around the publication of a new strategy to tackle hospital waiting times in Northern Ireland.