The payment was originally introduced by the Labour administration a decade ago.
Councillor Malcolm Cunning, the city’s Labour group leader, will bring a motion to this week’s full council meeting, which asks for the ‘affordable warmth’ payment to be reintroduced this financial year.
He wants the council to provide a “lifeline” to thousands of older people as energy prices soar.
The payment, introduced by a Labour council a decade ago, was scrapped earlier this year by the SNP administration, when its budget deal with the Greens was passed.
At the time, the SNP said the affordable warmth payment would be replaced by a Scottish Government scheme, and would include almost £5 million for the over 80s.
Labour believes reintroducing the payment would help tens of thousands of pensioners, and Councillor Cunning estimated the cost of the scheme would be at least £1.3 million.
He said: “Thousands of older people in Glasgow are struggling with their energy bills and face the horrific choice of heating or eating this winter.
“For years, the city council has provided a lifeline payment to the over-80s to help them through the winter months, recognising that nobody should be freezing in their own home.
“The SNP’s decision to scrap this was deeply regrettable, but there is now a chance to make amends.
“With prices soaring this is an immediate emergency, and as a council we must come together to help the most vulnerable in our city.”
He said there is a cost of living crisis caused by rising energy bills, the end of the furlough scheme and the UK Government’s decision to axe the £20 Universal Credit uplift.
The motion, to be presented to councillors on Thursday, states money to cover the affordable warmth payment should be taken from the council’s reserves, and future funding options should be included in a report after May 2022.
Councillor Cunning recognises pressures on council staff currently administering Covid-19 relief funds may delay the roll out of the payment, but it should be “disbursed as soon as practically possible”.
He will also call on the Scottish and UK Governments to introduce more support for vulnerable households
Nationally, Scottish Labour has called on the Scottish Government to launch a £70 winter fuel supplement for low-income pensioners and struggling families.
Council leader Susan Aitken had previously described the affordable warmth payment as a “lifesaver” but, in March, said it had been a “great policy for its time”.
She said money could be reinvested in “other ways to support people in poverty, including older people”.
The city’s SNP group has been approached for comment.