Clarkson was suspended by the BBC last month when he became the subject of an internal investigation after he attacked Top Gear producer Mr Tymon, splitting his lip and verbally abusing him.
Clarkson's contract was not renewed, with director-general Tony Hall saying "a line has been crossed" and "there cannot be one rule for one and one rule for another".
Clarkson has said he is already thinking about his next television project.
He wrote in his column for the Sunday Times: "I have lost my baby but I shall create another.
"I don't know who the other parent will be or what the baby will look like, but I cannot sit around any more organising my photograph album."
Clarkson also revealed he was told he "probably" had cancer, two days before the fracas with Mr Tymon, although he has since been given the all-clear.
He told the Sunday Times: "Let's stop being silly and pick up the pieces and start again ... I just know I'm going to do another car show."
- PAA