Mr Swinney told the Scottish Parliament’s Covid-19 recovery committee on Thursday that he would “dearly love” to rule these out, but that due to the rapid spread of Omicron further measures remain under consideration.
The Deputy First Minister was unable to give a final date for when these might come into force.
Asked by Scottish Conservative MSP Murdo Fraser if the Scottish Government was considering further restrictions, Mr Swinney said: “I would dearly love to be able to rule that out, but I can’t in all honesty do that at this stage.”
He added: “I hope that we can avoid applying any further constraints on the way in which people are able to enjoy Christmas.”
Mr Swinney reiterated advice given by Nicola Sturgeon on Tuesday, and urged Scots to limit their contact with other households before Christmas.
New Scottish Government guidance asks that social gatherings be limited to a maximum of three households.
Mr Swinney said: “I think that's the safest way to proceed, but I have to acknowledge that given the rapid pace of increase of Omicron cases, and the data that was shared by the Prime Minister and the chief medical officer in the United Kingdom yesterday, reinforces the point that the First Minister was making on Tuesday about the severity of the threat.
“I cannot rule out that we might have to apply further constraints in the period ahead.”
England’s chief medical officer Professor Chris Whitty told people to “prioritise what matters” in terms of social contacts before Christmas, in a press conference on Wednesday.
He said the UK was dealing with “two epidemics on top of one another” as a record 78,610 new cases of Covid were recorded.
Prof Whitty said: “I’m afraid we have to be realistic that records will be broken a lot over the next few weeks as the rates continue to go up.
“What we’ve got is two epidemics on top of one another – an existing Delta epidemic, roughly flat, and a very rapidly growing Omicron epidemic on top of it.”