A committee of "three wise men" has been set up to determine whether an honorary degree, awarded to Zimbabwe's Robert Mugabe, should be withdrawn.
The honorary degree was awarded by the university in 1984
A campaign was launched in April by politicians at Westminster to have the honour revoked because of the president's "oppressive regime".
He received the award from Edinburgh University in 1984 for his "services to education in Africa".
The senate, its highest academic authority, will now consider the issue.
In April, Nigel Griffiths, a former Labour minister, said he wanted it "swiftly withdrawn" amid continued concerns over the political situation in Zimbabwe and claims of human rights abuses.
A Commons motion, tabled by the former Edinburgh University student, expressed his "dismay" at the president's running of the country.
He said Mr Mugabe had "reduced his people to poverty, a state of terror" and had brutally suppressed opponents.
Zimbabwe has the world's highest annual rate of inflation - 1,700% - and only one person in five is in full-time work.
The motion was signed by fellow Labour MP Kate Hoey and is also supported by Edinburgh University's rector, Mark Ballard.
An Edinburgh University spokesman said: "The university is acutely aware of ongoing developments in Zimbabwe and the issue of Robert Mugabe's honorary degree remains under active review."