Lawyers for Clarkson and the BBC attended a closed-door hearing with Oisin Tymon's legal team at a London employment tribunal on Friday.
The case centres on "verbal abuse" that accompanied a physical attack during which Clarkson struck Tymon in March.
Clarkson, who was dropped by the BBC following an internal inquiry, will front a new show on Amazon Prime.
The inquiry, headed up by Ken MacQuarrie, found Mr Tymon was subject to an "unprovoked physical and verbal attack".
Lawyers Slater & Gordon confirmed on Friday that they had been engaged by the producer.
A statement by the BBC said: "We will be responding to this claim, but will not be commenting further at this time."
Witnesses
The assault took place at a North Yorkshire hotel, after Clarkson was told there was no hot food available at the end of a day's shooting on location.
As part of the inquiry, statements were given by two unnamed witnesses to the incident on 4 March.
The producer, who suffered swelling and bleeding to his lip in the altercation, drove himself to hospital after the incident believing he had lost his job.
BBC director general, Tony Hall, said Clarkson had subjected an "innocent party [to] a physical altercation accompanied by sustained and prolonged verbal abuse of an extreme nature".
At the time of the attack, Mr Tymon told police he did not wish to press charges.
In the days following the assault, he was the subject of sustained abuse on social media for his involvement in the dispute - prompting Clarkson himself to urge his fans to show restraint.
"I wish people would leave Ois alone because none of this was his fault," the presenter told reporters in March.
Clarkson will be joined by his erstwhile Top Gear co-hosts Richard Hammond and James May on a new show for Amazon Prime, to be broadcast next year.
The Irish Top Gear producer punched by Jeremy Clarkson is suing the presenter and the BBC for racial discrimination.