The Daily Record has reported a leaked document detailing proposals from the Scottish Government to extend the break further into January.
The memo said a plan to extend Christmas holidays from December 18 to January 11 was discussed at the Scottish Government’s Education Recovery Group meeting on Thursday.
It comes amid concerns there could be another spike in coronavirus cases in January after the four UK administrations gave the go-ahead for a limited relaxation of restrictions over the festive period.
Many fear this easing of measures, which runs from December 23 to 27, will lead to more infections.
The Health Secretary confirmed the idea of extending the school holidays is being considered with unions and local authorities.
Ms Freeman said: “They’re looking at the festive period and the school holidays, and how we return to school at the end of that period.”
She stressed no final decisions have been made on extending the Christmas break for pupils.
Her comments came as the latest daily coronavirus figures showed there have been 37 deaths and 969 positive tests recorded in the past 24 hours.
As a result, the number of people who have died within 28 days of testing positive for the virus has now risen to 3,676.
Ms Freeman said: “We’re very conscious that of course parents and teachers and kids at school want to know what is going to happen, and we will make sure we reach a view, based on the advice from the Expert Recovery Group, and make sure that we reach a view as soon as we can so that people do have advanced notice.
“We want to give people as much notice as possible if there is to be any change at all.
“But at this point that decision hasn’t be made.”
She also stressed the Scottish Government is focused “absolutely on the importance of keeping our schools open”.
Ms Freeman said: “We value very highly indeed the opportunity that gives our young people to pursue their education.
“Closing schools, as we had to do at the time when that happened, did have an impact, not withstanding the huge efforts teachers, parents and pupils themselves put into maintaining their learning.”
Campaign group Us For Them Scotland said it is “vital” youngsters do not lose out on time in the classroom.
Organiser Jo Bisset said: “If schools do close for an additional week over Christmas, then that time must be made up in the spring.
“Parents understand that the festive period will be complicated for everyone, not just the schools system.
“And while this will undoubtedly cause difficulty for many from a childcare perspective, that will be eased somewhat by a guarantee that their children won’t miss out overall.”
Us For Them Scotland pressed the Scottish Government for a return to full-time schooling for all youngsters in August, with ministers abandoning previous plans for blended learning.
That option would have involved pupils spending part of the week in school, while learning at home for the rest of the time.
Ms Bisset said: “Blended learning doesn’t cut it – that was made painfully clear during the first lockdown.
“The solution to an extended winter break can only be additional days put back in the calendar before the crucial end-of-term exams.”