The former Prime Minister will be in the city to make a speech as part of the Better Together campaign for a No vote in September's referendum on independence.
He will say pensions are one reason where the "pooling and sharing of resources" across the UK benefits Scotland,
Mr Brown will say there is a faster growing elderly population in Scotland but because pensions are funded according to need and not based on population share, north of the border benefits from a faster rising working age population than the rest of the UK.
He will be speaking at Glasgow University on an internal Department Of Work And Pensions document on the rising cost of pensions. The paper states the numbers of Scots pensioners will increase over 20 years and the extra benefit Scotland gets from UK funded pensions will rise from £435million a year to £700m a year.
Mr Brown is expected to say: "The whole point of sharing risks and resources across the UK is that it is right and proper that the British welfare state bears the rising cost of Scottish pensions as the number of old people will rise from 1m to 1.3m.
"As the DWP document makes clear, it is fairer and better for everyone that Britain's faster rising working-age population rather than Scotland's slow rising working-age population covers the cost of the rising numbers of elderly in Scotland, because we have contributed in UK National Insurance all our lives to spread the risks of poverty in retirement."
Mr Brown believes the SNP recognises pensions is a difficulty for an independent Scotland.
He will say: "If the SNP deny there is a problem they have to explain why they have set up a working party on 'the affordability' of future pensions. It makes no sense either to break up the British system of pension payments or to set up a wholly new administrative system that the DWP costs at £1billion in the first years."
The DWP paper states the pensioner benefits per head of population in Scotland is £1805, against £1725 for the UK as a whole.
Mr Brown will say: "The SNP Government has said the case for independence should be judged on whether Scotland would benefit financially or not.
"It is clear pensioners are better protected when the risks are spread across the UK."
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