The Educational Institute of Scotland (EIS) says six of its branches are moving to ballot union members in disputes with their local authorities, while another four branches are considering whether to take this step.
It follows EIS claiming that current coronavirus measures do not keep pupils or staff safe.
The union is calling for more remote teaching and learning to be used before and after the Christmas break with a proposed shift to remote working for a few days around the festive period.
EIS general secretary Larry Flanagan said: “The Scottish Government and local authorities seem determined to keep schools physically open, at all costs, right up to Christmas.
“Scotland’s teachers are clear that this will present a very real risk to their health, their pupils’ health and the health of their families by increasing the risk of Covid-19 spreading through family festive gatherings.
“Making a very slight change to arrangements around the holiday period, by allowing teachers and students to work remotely from home for a few days, would significantly reduce the risk of pupils or staff taking the virus into their family groups in the festive period.”
A Scottish Government spokesman said: “We recognise that this is an anxious time for teachers, families and pupils and we are grateful to all school staff for their dedication and hard work during a very challenging time.
“The safety guidance on reducing the risks of coronavirus in schools includes robust measures to help us to protect teachers, pupils and the whole school community.
“The Health and Safety Executive provided very positive feedback on the way schools are implementing that guidance and we are monitoring the situation closely, along with emerging scientific evidence.”
He continued: “There is no current direct evidence that transmission within schools plays a significant contributory role in driving increased rates of infection among children and ONS data has shown no evidence of any difference between the positivity rates of teachers and other school staff, relative to other worker groups of a similar age.
“We continue to have discussions with teachers, trades unions, local authorities, parents and young people as we move through the coronavirus crisis.”