The money would pay for insulation measures and other improvements such as solar panels, batteries, and low carbon heating to help cut bills, reduce fuel poverty and lower carbon emissions.
The council is also waiting to hear if it has been awarded more than £34m from the Warm Homes: Social Housing Fund.
This money would be match-funded with £29m from the council.
The funding would pay for energy efficiency improvements to around 2,700 social houses over the next three years.
Work would include loft and cavity wall insulation, air source heating, low energy lighting and solar panels.
The funding was welcomed by senior councillors and offices at the authority’s executive committee meeting this week.
Councillor Simon Myers, executive member for culture, arts and housing, said: “This a real opportunity for our residents particularly, our most vulnerable residents, to tackle what we know is a scourge across North Yorkshire which is fuel poverty.
“The fact is that so many of our residents live in pre-1970s housing that has very little insulation, so this is a real positive for our residents which will leads to warmer homes and smaller heating bills.”
Cllr Myers said the two funds together would equate to a £90m investment in energy efficient measures.
He added: “That means skilled jobs, it means well-paid jobs, it means an opportunity for our young people to develop the skills that are going to be needed in this sector for 30 years.
“Providing the government gives us the money we’ve asked for; this is a real win-win for North Yorkshire residents.”
Councillor Greig White, executive member for managing our environment, also welcome the funding.
He said: “This is actually about stopping waste so it’s just good in every respect because it helps the environment and it also helps those individuals in these homes lead better lives because they can be warmer.”
The government is expected to announce if the council has been awarded the funding for social housing shortly.
The council would have until September 2028 to complete the work if successful.