The Department of Education (DE) is considering two-week summer schools for pupils going into Years 5 ,6 and 7.
The department wants to gauge interest from primaries and community organisations about whether they can hold the schools in late July.
However, no school or organisation will be required to do so.
"This is subject to funding being available and with the agreement of the executive, teaching unions and schools," a DE spokesperson said.
More details are contained in an email from departmental officials seen by BBC News NI.
It suggests asking primaries if some teachers would be willing to run a summer school for two weeks from 20 July to 31 July.
Schools would be asked how many pupils they could take on an estimated ratio of one teacher for every seven pupils, so that Covid-19 safety precautions would be followed.
The department email said that food and cleaning costs would be covered, as well as other financial support - if funding was available.
"The department may provide financial support to any schools who wish to run their own summer schools this year for current Year 4, Year 5 and Year 6 pupils," the email continued.
"We want to make clear this is a voluntary offering for those who wish to avail of it and there is absolutely no requirement to run a summer school."
The department is planning to ask primaries if they would be interested in running such a summer school, as part of their existing survey of how many schools are open and how many pupils are attending them.
Among the other proposals the department is considering is extra online lessons in literacy and numeracy for some pupils going into year 7.
Children taking the extra lessons would also get online support from a substitute teacher.
Schools would be asked to identify pupils going into year 7 who may need extra support and have "appropriate" IT access, in the first instance.
However, neither scheme is yet finalised.
A Department of Education spokesperson said Education Minister Peter Weir had asked departmental officials to develop proposals for summer schemes.
"A limited number of schools and community organisations may be seeking to support children for short periods over the summer, and any practical support will be considered," they said.
"The schemes will be managed by participating schools and community organisations and will be on a voluntary basis.
"There may also be scope for virtual learning support for some pupils.
"This is subject to funding being available and with the agreement of the executive, teaching unions and schools."