Mr Swinney currently has a wide remit encompassing the constitution, Government strategy and intergovernmental relations as well as his finance minister role monitoring the economy, fiscal policy, the Scottish budget, spending, taxation and public pay.
He said there is “undoubtedly an argument” for a chancellor-type role in Scotland solely in charge of pulling the purse strings.
Mr Swinney also welcomed the UK Chancellor’s tax reliefs on the oil industry as “helpful”, and said the Scottish Government is “broadly supportive” of George Osborne’s sugar tax.
Speaking at a Scottish Parliamentary Journalists’ Association event in Edinburgh, Mr Swinney said: “There is an argument for there purely being a ministerial role that looks solely at the issues of tax and public expenditure control.
“There are other responsibilities of course. The responsibilities in this respect will be growing very dramatically in the course of the next few years.”
He added: “What has changed, and what I thought was quite evident in the Budget process in the last couple of years, was the growing proportion of time and budget preparation that is now taken on tax-related issues.
“It opens up a very significant new set of issues and the deployment of responsibilities within government must be considered within that backdrop into the bargain.”
He said a Scottish chancellor is “an interesting prospect worthy of further consideration given the nature of how our responsibilities are changing”.
He insisted the economic argument for Scottish independence remains sound, despite Mr Osborne’s warning that Scotland would have faced “the highest deficit in the western world” next week if the nation had voted Yes.
Mr Swinney said: “Yes, we have got a particular challenge at the moment around oil but we also shouldn’t lose sight of the fact that over a very long period of time, oil has contributed very significantly to the UK economy, and in the years to come there is still a very significant economic opportunity in the North Sea sector.
“That to me is where the economic case for independence rests, given the fundamental inherent strength of the Scottish economy.”
On the Chancellor’s oil industry relief, Mr Swinney said: “What he did yesterday was helpful.
“I think given the scale of the challenge that we currently face I think the Chancellor could have done more to reduce the cost to individual companies and give them the greater ability to weather what is a very difficult period.”
On the sugar tax, he said: “We support tax measures that can have an effect on people’s behaviour and wellbeing.
“Our stance on minimum pricing is an indication of what we think in relation to alcohol.
“So taking that logic and rationale to the proposal that the Chancellor set out yesterday, we would be broadly supportive of that.”