Mr Swinney said new coronavirus restrictions could be introduced next week, with a statement due on Tuesday.
Ministers were spending the weekend "wrestling with the challenge of what are the right rules to have in place", he added.
But he said he does not think that Scots will face a restricted Christmas.
Asked on BBC Breakfast if new Covid-19 measures would be put in place next week, Mr Swinney said: "I can't say definitively that will be the case, but that's certainly been looked at over this weekend.
"And we have to judge what's the best set of measures that we can take to try to interrupt the circulation of the virus. We can't have it moving at the pace its moving at just now because the danger is that will overwhelm our public and private services."
First Minister Nicola Sturgeon is due to give a statement in the Scottish Parliament on Tuesday.
On Friday, she told a televised press conference that Scotland faced a "tsunami" of Omicron cases.
Mr Swinney's comments come as the latest statistics show 11 more Omicron cases have been confirmed in Scotland, taking the total to 121.
There were 4,087 coronavirus cases in total reported in the last 24 hours, with 12 deaths.