Snowden is expected to take over as lord rector of the school in place of departing former Liberal Democrat leader Charles Kennedy, the newspaper reported Tuesday.
As lord rector, Snowden is responsible for representing the interests of students to university management.
He was encouraged to take the position by a group of students who contacted his lawyers.
Snowden currently resides in Russia after seeking temporary asylum last year after exposing NSA data collection techniques and other classified material.
Some students have criticized the move since it's unlikely Snowden would even be able to visit the campus. Rectors are expected to regularly visit the campus and meet with staff and students, the Independent reported.