It comes as the Scottish Trade Union Congress warned the reform was “sailing perilously close to the wind” after the Unite union pulled out of the design process.
Mr Swinney also warned there was still £100m worth of savings required in this financial year to ensure the Scottish Government can balance its Budget, as it is legally required to do.
Speaking at the Scottish Parliament’s finance committee, the deputy first minister said that final gap was likely to be closed as risks to additional spending within the financial year either become clearer or disappear.
Before Christmas, Holyrood finance watchdogs, including SNP MSPs, expressed “significant concerns” over the lack of detailed costs for the National Care Service (NCS), with the finance committee questioning its affordability and sustainability.
The reform is viewed as a flagship reform for the SNP/Green government, with Nicola Sturgeon describing it as the “most significant public service reform” since the NHS was created.
Committee convenor, SNP MSP Kenny Gibson, pressed Mr Swinney to provide a figure for the cost of the NCS in the coming financial year, stating one was needed to counter “wildly differing figures” of how much the reform will cost.
Mr Swinney said: “We have made provision in the budget for a range of measures in relation to the NCS, not least of which is the increase in the social care payment rates, which amounts to a substantial part of the journey we are trying to undertake on the NCS to increase the remuneration of social care staff so that career is a more attractive proposition.
"I think the maximum cost in terms of the next financial year is likely to be a figure no higher than about perhaps £50m. The financial memorandum will give greater confidence around that point.”
The Scottish Government’s financial memorandum on the cost of the NCS, published in June last year, estimates the cost at between £664m and £1.26bn over five years to establish the service.
For 2023/24, the reform was estimated to cost between £63m and £95m, with the £50m set to underline a cut to the expected spending on the reform.
Labour MSPs Carol Mochan and Monica Lennon attacked the new figure, with Ms Lennon posting on Twitter: “Is there a zero missing?”
Ms Mochan added: “Our worst fears about the NCS are coming to pass. The SNP don’t believe in serious reform and radical change, it’s all just talk.”
The NCS has been beset by opposition from local government, which has labelled it a power grab by SNP ministers, and by unions with Unite pulling out of the plans in recent weeks.
General Secretary of the STUC, Roz Foyer, told The Scotsman: "It's abundantly clear that the future of the National Care Service is sailing perilously close to the wind.
"We are strongly reiterating to the Scottish Government that, whilst supportive of the destination, we cannot endorse the current trajectory of the NCS, one that rewards private profit within a supposedly public care system.
"Our NHS and social care staff are barely keeping it together in a pandemic-ravaged sector starved of sustained funding. The solution is simple – pause the NCS Bill and reallocate funding direct to the front-line, giving our social care staff the support they desperately need”.