Lawyers for the 55-year-old presenter and the BBC had a closed-door hearing with Tymon’s representatives at a London employment tribunal yesterday, according to sources.
Clarkson, who was later fired by the BBC, reportedly called Tymon a “lazy, Irish c***” during a confrontation at a hotel in north Yorkshire.
Tymon’s law firm Slater and Gordon said it would not comment on the case.
A BBC spokeswoman said: “We will be responding to this claim but will not be commenting further at this time.”
Clarkson was suspended after the “fracas” over catering on March 10, and was sacked by the BBC on March 25, following an internal inquiry.
The inquiry, led by the director of BBC Scotland Ken MacQuarrie, said Tymon “was struck, resulting in swelling and bleeding to his lip” during the “unprovoked physical and verbal attack”.
Mr MacQuarrie added: “The verbal abuse was sustained over a longer period, both at the time of the physical attack and subsequently.”
Since his departure from Top Gear, Clarkson has signed a deal with Amazon Prime to present a motoring show, which will air in 2016.
He will be joined by his co-presenters from the BBC show, Richard Hammond and James May, as well as producer Andy Wilman.
Britain’s newspapers reported at the time that the row was over a missing meal and that Clarkson had called Tymon a “lazy, Irish c***”.
Clarkson, 55, reported himself to BBC management after he admitted giving Tymon a bleeding lip, for which the producer sought hospital treatment.
The presenter had repeatedly landed in hot water with the BBC before, particularly for repeated use of racial slurs during his shows.
Last year, the team fled Argentina after residents hurled stones at a Porsche driven by Clarkson whose licence plates appeared to refer to the Falklands War.