The enquiry is being headed up Ken McQuarrie, the director of BBC Scotland.
Jeremy Clarkson, 54, was suspended from Top Gear last week following an alleged altercation with producer Oisin Tymon.
Oisin Tymon, 36, did not file a formal complaint and its understood that Jeremy Clarkson reported the incident himself.
The row has been said to have occurred because no hot food was laid on for Jeremy Clarkson following a day of filming in North Yorkshire.
Writing in his column in the Sun newspaper, Jeremy Clarkson appeared to hint that he was close to quitting calling himself a “dinosaur” and adding: “These big imposing creatures have no place in a world which has moved on.”
An online petition to reinstate Jeremy Clarkson has reached more than 900,000 signatures.
The critic AA Gill also voiced his support for Jeremy Clarkson in his Sunday Times column, calling the investigation into the row “preposterous and ponderous”, and praised Clarkson as hard-working.
Top Gear is one of the BBC’s most popular and profitable TV shows, with an estimated global audience of 350 million.
The remaining shows in the current series were pulled off-air following the incident.
A lawyer for Oisin Tymon said his client “intends to await the outcome of the BBC investigation and will make no comment until that investigation is complete”.
No official date has been fixed for the investigation to present its findings.
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