Northern Ireland's Education Minister Peter Weir wants post-primary schools to consider running summer schools for some pupils this year.
The Department of Education has written to schools to ask if they are planning to open over the summer.
In 2020, about 50 primaries and 20 special schools held summer classes for some pupils.
Most pupils have been out of school in Northern Ireland since December though the youngest are due back on 8 March.
However the Stormont executive has decided that many children will not return to school until after the Easter holidays at the earliest.
In 2020, about 50 primaries in Northern Ireland held two-week summer schools for some pupils going into years five, six and seven.
That was due to concerns that the education of some children had been harmed as they had not been able to physically attend school for a number of months.
The Department of Education has now written to schools to ask if they will hold similar classes this year.
But they said that Mr Weir wants to expand the scheme to post-primary schools.
'Deserve their summer break'
"In view of the positive response last summer, Minister Weir wishes to explore the level of interest in a similar programme this year, should funding be made available, with an expansion to post-primary and education other than at school settings," the department's letter said.
"We know that teachers and school principals have been under continuous pressure for two years dealing with the out-workings of Covid-19 and deserve their summer break.
"At the same time, we know that many children have been significantly impacted by long periods of lockdown and could really benefit from the opportunities to meet their friends, take part in physical and fun activities outside and get the emotional health and wellbeing support they might need."
The department said that the 2021 scheme would focus on "emotional health and well-being, being physically active and reconnecting and rebuilding relationships with friends, with teachers and other adults in school".
They added schools should let them know by 5 March if they were willing to open for some pupils over the summer.
Northern Ireland's mental health champion Prof Siobhan O'Neill has previously called for all children and young people to be offered a summer "wellbeing" scheme this year.