John Swinney said on Thursday that the Cabinet will meet as it usually does on Tuesday to discuss restrictions across the country, but could not rule out the imposition of strict new measures in Scotland.
According to Mr Swinney, cases are beginning to rise again in Scotland, with 99 cases per 100,000 people 10 days ago increasing to 116.
"Unfortunately, in Scotland today, we are in a rising tide of coronavirus cases," he told the BBC.
"The less we do to have social interaction in the period going forward, the better, in terms of stemming the rise in coronavirus cases within our community."
The Welsh Government announced on Wednesday that tougher restrictions will be imposed on the country immediately after the Christmas easing period, which is due to end on December 27.
Asked if the Scottish Government is considering similar measures, the Deputy First Minister did not rule out the idea of a lockdown or tougher restrictions.
"We'll have to look at what the forward prospects look like, we'll have to take decisions that will be sustainable for a period into January and February to protect the public interest and protect the National Health Service," he said.
Asked specifically if there could be greater restrictions or a possible lockdown, he said: "That could be a possibility, I can't rule it out.
"We are on a rising tide of coronavirus cases.
"We will be looking, as we always do, at what the outlook is based on the data in front of us, and we have to take decisions, difficult decisions to make sure we protect the public from a highly dangerous virus."
Mr Swinney also said it is too early to say if areas of Scotland will be moved into higher levels of protection when the Cabinet meets on Tuesday, a session that is not expected to go ahead over the Christmas period, but was announced by the First Minister on Tuesday in Parliament.
Reporting by PA