Finance convener Alasdair Rankin admitted measures which had previously been rejected were now to be re-examined.
It is understood cutting school budgets is another move which councillors were unwilling to approve but will now consider again.
Figures published in the wake of Finance Secretary Derek Mackay’s budget last week show Edinburgh must find £39m savings to make the books balance rather than the £28m it expected.
The Evening News revealed in September that officials had put forward a series of possible cuts which the SNP-Labour administration was considering, including “significantly” reduced opening times for libraries, a cut of up to three per cent in budgets handed to school heads and halving music tuition, as well as closing almost all the city’s public loos, reducing spending on road repairs and street cleaning and stopping emergency repairs.
Cllr Rankin said with more savings needed, new areas were now being considered for cuts. “Given that we are looking at having to find more savings than initially expected there has been a fresh range of proposals put forward to us by officers.”
But he said a political decision on which ones to take forward would not be made until the new year.
And he said: “We may have to go back to things in the full set of measures. There are some things we would rather not do but it may be we have to look at one or two of these things. We might be looking at the possibility of more limited opening hours for libraries.”
But he stressed: “There is an extreme reluctance to look at the idea of closing libraries. It is an element of provision that is extremely important and would have a real effect on people’s lives.”
A source claimed the cut to school budgets was also back on the agenda, but cuts to music tuition had been ruled out after Education Secretary John Swinney spoke out against such a move.
Cllr Rankin is still hoping that talks at Holyrood between the SNP and Green MSPs to secure their support for the government budget could lead to more cash being found for councils.
He said: “It’s not clear whether negotiations will change things in the way they did last year. Our figure then was just over £12m which was undoubtedly a great help.”
But he said the council had to prepare on the basis of the figures in the government budget.
“In the past we have produced a range of measures and ranked them with the least desirable at the bottom. If more money does come forward we then move the line so we can avoid doing things we would rather not do.
“We are legally obliged to achieve a balanced budget, but we will put forward what we regard as the least painful set of measures. And we will maintain services to the greatest amount possible.”
Detailed cuts proposals are due to be made public towards the end of January before the budget is set in February.