Kanhaiya Kumar was arrested last month, after a rally against the execution of a Kashmiri separatist convicted over the 2001 Indian parliament attack.
A panel from Jawaharlal Nehru University (JNU) probing the incident reportedly recommended the expulsion of five students, including Mr Kumar.
Mr Kumar was released from jail after being granted bail earlier this month.
His views have been divisive in India with some calling him "anti-national".
Kanhaiya Kumar: India's most loved and loathed student
The Press Trust of India news agency reported that the university panel had found the students guilty of "violating university rules and discipline norms".
Apart from Mr Kumar, the panel has also reportedly recommended the expulsion of Umar Khalid and Anirban Bhattacharya, two other students who remain in custody.
Reports say a final decision on the panel's recommendation will be taken by the vice chancellor of the university.
Authorities allege Mr Kumar and others shouted anti-India slogans at the 9 February rally on the campus.
Critics have condemned the charges against the students as an assault on freedom of expression, but government ministers have refused to back down, vowing to punish what they describe as "anti-national elements".
The rally that prompted the arrests was to mark the third anniversary of the 2013 hanging of Mohammed Afzal Guru.
Guru was one of those convicted of plotting the 2001 parliament attack - charges he always denied. The attack, which left 14 people dead, was blamed on Pakistan-based militants fighting Indian rule in Kashmir.
Indian opposition parties see the affair as an attempt by the BJP to push its Hindu nationalist agenda, correspondents say.
There have also been counter protests by those who say JNU is a hotbed of "traitors" and should be "cleaned up".

Thousands of miners and police clashed at the South Yorkshire coking site.
Campaigners met with Home Secretary Amber Rudd to renew calls for a probe into police handling of the event.
It comes after an ex-PC told Channel 4 officers were told to write statements for arrests they had not made.
He said: "I knew in my own mind that was wrong."
A delegation from the Orgreave Truth and Justice Campaign (OTJC), which met with the Home Secretary, said they were feeling "positive" after the meeting.
The so-called Battle of Orgreave saw miners attempt to stop lorry loads of coke leaving for the steel works, with police holding them back.
About 6,000 officers are alleged to have used excessive force to suppress the miners' strike at the plant.
What was the 'Battle of Orgreave'?
Shadow home secretary Andy Burnham, who was also in attendance, said it was an "encouraging meeting" and he hopes a decision will be made to "shine a spotlight on our country's past".
Former miner Kevin Horne said: "I think we have reached another milestone. There's still a way to go, but we're getting there."
Earlier, Labour leader Jeremy Corbyn and other MPs gathered for a demonstration outside Parliament to lend their support.
Veteran Labour MP Dennis Skinner, who was at Orgreave, said: "The police at Orgreave were called upon to write the same thing over and over again about every single miner they arrested."
A total of 95 miners were charged following the clashes but their trial collapsed.
A student leader from a top university in India charged with sedition may be expelled from campus, reports say.
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Campaigners calling for a public inquiry into the 1984 Battle of Orgreave disorder have been told a decision will be made by the end of October.