Holyrood ministers say Scotland, which has a proportionally larger public sector than the UK as a whole, needs more than £500m to compensate for increased public sector staffing costs.
It is understood the Treasury has proposed a payment of about £300m. SNP Finance Secretary Shona Robison said she would not "settle" for that figure.
The UK government says Holyrood is receiving more money than ever before from the Treasury in the next financial year.
There is also tension between the governments over a Scottish Budget proposal to effectively scrap the two-child benefits cap north of the border.
The UK-wide policy was originally introduced in 2017 by the Conservative government and has been kept in place by Labour.
It prevents parents from claiming universal credit or child tax credit for a third child, with a few exemptions.
Swinney said he wanted to end the "heinous" two-child limit "because the UK Labour government has to date failed to do so".
However, he will require assistance from the Department for Work and Pensions to create a system that will allow Holyrood to provide funding to the families of 15,000 affected families in Scotland.
Sir Keir said he was committed to tackling child poverty, but said scrapping the cap was not a "silver bullet".