The board is also reportedly considering banning players from making appearances on such 'non-cricket' shows altogether.
A group of MPs wants to demand an investigation into misgovernance by the JNU administration under the vice chancellor.
The varsity administration and the JNU teacher's association has been at loggerheads over the issue of compulsory attendance for teachers.
According to the JNUSU, N. Sai Balaji is facing two enquiries. The first one for raising "anti-Modi, anti-VC and anti-RSS" slogans outside an Academic Council meeting.
An informal report compiled by the students alleged rampant "moral policing" by security personnel, non-academic staff, faculty and fellow students.
Last week, the students' union had accused the varsity administration of cutting down library funds from Rs 8 crore to Rs 1.7 crore.
JNU's administration appears to be complicit in this process and failing in its duty to defend its own university and its democratic culture, said the teacher's association.