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".
A student leader from a top university in India charged with sedition may be expelled from campus, reports say.