Excerpts of the one-hour documentary show the two lecturers in compromising situations with undercover journalists who had posed as students of the University of Ghana.
Dr Butakor, who is a lecturer at the College of Education is seen in the video allegedly having inappropriate with the "student" by asking to be her "side boy".
Prof Gyampo, who is also the Head of European Studies at the university, according to the BBC report allegedly proposed marriage to the "student" who was seeking academic favours.
In excerpts of the video released on BBC Somalia’s Facebook page, Professor Gyampo persuaded the reporter to meet him at the mall where he was caught on camera making “numerous [alleged] inappropriate demands.”
In the report, he also allegedly requested to kiss the reporter.
Meanwhile, Prof Gyampo in a reaction in a radio interview with Accra based Citi FM, has threatened to initiate legal action against the BBC.
He told Citi FM: "You've also seen the video, have you seen anything called sex for grades [in the video]. How can you engage in so called sex for grade relationship with somebody who is not a student in the first place."