Mr Swinney will deliver his sixth Budget in Holyrood today after he warned that cuts from Westminster meant the Scottish Government could not do all it wanted and is unable to mitigate all the welfare cuts implemented from the UK Government.
He has said his Budget will be focused on promoting economic growth and protecting and creating jobs.
The latest unemployment figures showed Glasgow with a higher jobless rate than the rest of Scotland at 10.9%, against 8.2%.
Council and business leaders called on Mr Swinney to reveal measures to ensure growth and jobs for the city.
Gordon Matheson, Glasgow City Council leader, said: "I hope Mr Swinney uses his Budget speech to announce new powers for cities, in line with those in the rest of the UK.
"I am concerned that Glasgow and other major cities in Scotland are being left behind our UK counterparts.
"I would like to see greater freedom to keep business rates, invest in growth and create jobs.
"I also want to see the acceleration of capital investment in the city, and hope to hear details from the Scottish Government on how it will use its considerable powers to support our citizens who will suffer from welfare reforms."
The Evening Times reported last week that Mr Swinney said the scale of welfare cuts from the UK Government was so severe, Scotland could not prevent them affecting lives.
Business leaders are calling for more investment in infrastructure and tackling skills shortages.
Stuart Patrick, chief executive of Glasgow Chamber of Commerce, said: "It must be a Budget for jobs.
"The skills budget has to be aligned more closely with where the job opportunities are.
"There are shortages in financial services and engineering, with not enough graduates coming through for the long-term opportunities we have.
"Capital spending needs a boost. The projects we have had are all welcome, but are still not enough to get the construction industry off its knees."
First Minister Alex Salmond, who met Premier David Cameron in London last week, warned a lack of action from Westminster and the inability of Scotland to borrow to fund projects was harmful to the economy.
He said: "We recognise action around investment is required now – not in three years.
"That is why I have again urged the Chancellor to perform another Budget U-turn by announcing an extra £5billion in capital investment, which would allow us to provide an additional stimulus of more than £400million to support employment in Scotland now."