Mr Swinney, the deputy first minister in the last Scottish Government, said it was an “aspiration” for the virus to be consistently suppressed by the end of the year to meet their conditions for another vote on independence.
First Minister Nicola Sturgeon has argued there should be a second Scottish independence referendum once the country emerged from the immediate crisis of the Covid-19 pandemic.
Scotland returned a majority of pro-independence MSPs at last week’s Holyrood elections, with 64 SNP representatives and eight from the Scottish Greens.
The SNP manifesto said that another vote on independence should be held before the end of 2023 if the Covid-19 crisis was over.
Asked how that would be determined, Mr Swinney told the BBC Good Morning Scotland programme it would be when coronavirus has been consistently suppressed and the vaccine and testing systems are operating effectively.
He said: “We judge it by a combination of things – the actions that we’ve got to take to suppress the prevalence of the virus, and to make sure that we are in a stable position.
“Secondly, that we are able to sustain that position to make sure that we’ve got the necessary infrastructure in place to ensure that the virus is suppressed.”
Mr Swinney added: “If the pandemic meets those tests, then obviously we are able to consider the whole question of the timing of the referendum on independence.”
With the vaccine programme due to vaccinate the vast majority of the population over coming months, Mr Swinney suggested it was an “aspiration” the tests for focusing on another referendum could be met by the end of this year.
Adding a note of caution, he continued: “But I can’t sit here today and see that will be the case because within a relatively short space in time a situation can become very serious – as it has become in Moray.
“So we have to maintain constant vigilance and make sure that we have that sustainable position in place.”
He added: “I think we’re moving into a period where Covid becomes much less of an immediate epidemiological threat to the population, because of the measures that we have successfully taken to suppress it.”
Earlier on the programme, Scottish Conservatives leader Douglas Ross argued the SNP should focus on the pandemic and delivering its manifesto pledges that are “within the remit of the Scottish Parliament” – rather than pushing for a referendum.
Mr Ross suggested another referendum would create “uncertainty and division all over again” and said: “We need unity.
“We’ve been united together as a country to come through this pandemic and I think people expect their politicians to be united in dealing with the big challenges that we face in the weeks and months and years ahead.”
He added “I think people across Scotland really expect their politicians and MSPs and all political parties to focus on using the powers that we currently have here in Scotland.”
Former prime minister Gordon Brown also urged Ms Sturgeon to answer questions on what independence for Scotland means on issues such as costs and the border.