Currently, students in Northern Ireland receive maintenance loan and grant payments three times a year, usually at the beginning of each academic term.
Student leaders say that making the payments monthly would help students make ends meet more easily.
DEL said it would cost between £250,000 and £350,000 to implement the changes.
Most students in Northern Ireland take out a loan to cover living costs, but many also receive additional support grants.
Unlike loans, the grants are means tested and do not have to be repaid.
In 2013/14 over 42,000 students in Northern Ireland borrowed a total of £131m in maintenance loans.
However, just under 25,000 students - around 60% - were also given a support grant to help with living costs, costing DEL just over £68m.
The level of grant a student receives depends on household income.
If it is £19,203 or less, students are eligible for the maximum grant of £3,475 a year.
However, students coming from households where the total income is between £19,203 and £41,605 receive a partial grant, and in 2013/14, 38% of students in Northern Ireland got the full grant and 22% received a partial grant.
Like maintenance loans - where a student gets £3,750 a year if they are living with their parents and £4,840 a year if they are living independently - the grants are paid in September, January and April.
However, a monthly system is currently operating in Scotland, where students get a relatively large initial payment in September, followed by smaller monthly payments from October to June.
NUS-USI President Fergal McFerran said that monthly payments would be better for students.
"Having monthly support payments, with the September payment being larger than the other 11 months, could help students pay for accommodation deposits, household equipment or study materials that they need to buy at the start of the academic year," he said.
However, there is no indication that the level of maintenance loan or support grant is set to rise.
Launching the consultation, DEL Minister Stephen Farry said: "While there is little flexibility in the current financial context with the overall level of support available to students, there is scope to consider the profiling of that support."
The consultation closes on Sunday 27 September.
Tuition fee loans, currently at £3,805 per year for a Northern Irish student studying at Queen's or Ulster University, are paid directly to the university and would not be affected by any changes.
The Department for Employment and Learning (DEL) has launched a consultation on whether grants should be paid to students every month.