Education Minister Peter Weir wants all pupils in Northern Ireland back in classrooms by 12 April after the Easter holidays, BBC News NI understands.
The proposal is included in a paper from Mr Weir to executive ministers.
It also recommends that all primary school children who have not yet returned to school (primaries four to seven) should start on 22 March.
That is the same day students in Years 12 to 14 are due to resume face-to-face learning.
The Stormont executive will meet on Thursday to discuss Mr Weir's proposals but will need to consider them in line with advice from health officials.
Mr Weir has also said he wants to scrap the current plan for students in primaries one to three, who returned to class on Monday, to revert to remote learning on 22 March.
The minister argued that plan did not make "enormous sense" and that those year groups should be allowed to continue with face-to-face learning.
Department of Health advisers previously warned against a full return of schools like in England, instead recommending a phased approach.
Earlier on Tuesday, Finance Minister Conor Murphy said the executive wanted to ensure all children in Northern Ireland could return to school as "quickly as possible".
Asked by DUP assembly member Paul Givan if he would support the education minister's proposals, Mr Murphy said he would be guided by health advice.
"All ministers want restrictions lifted as soon as they can, for a variety of reasons," he told the assembly.
"Online learning is no substitute for face-to-face learning, as everybody recognises.
"Of course we want to do it as quickly as possible as to what's safe at the time over the course of the pandemic and the transmission rates associated with that."
Speaking at a press conference in Belfast, Health Minister Robin Swann said he would not pre-judge the outcome of the discussion ahead of Thursday's executive meeting.
First Minister Arlene Foster said the ministers would consider health advice, in conjunction with other harms before reaching a decision.