The Top Gear presenter sparked outrage after declaring on The One Show this week that he would "execute" protesting workers in front of their families.
Clarkson said that he was "happy to apologise" for his remarks, although The Mirror claims that the 51-year-old previously appeared reluctant to back down when speaking to its reporters yesterday.
Clarkson is quoted by the publication as explaining that he was trying to mock the BBC stance on impartiality by expressing "an extreme version" of an alternative viewpoint.
"What I was actually doing was presenting two different opinions for the BBC's impartiality," he said. "I support the strikers in the first part. I said it was like being in the '70s, my favourite decade.
"Then I said, 'But this is the BBC so we have to be impartial' and I expressed an extreme version of the other side of the coin, neither of which I believe.
"I expressed two different views. Which one do I apologise for? I am just making fun of the BBC's need to be impartial. Not about strikers. I wasn't saying that strikers should be shot."
The BBC confirmed today (December 2) that it has received over 21,000 complaints about Clarkson's comment, which was apparently cleared by the One Show production team.
The corporation released a statement saying: "As has now been widely reported, we had many complaints about a number of Jeremy Clarkson's comments on the show.
"The One Show is a live topical programme which often reflects the day's talking points. Usually we get it right, but on this occasion we feel the item wasn't perfectly judged.
"The presenters apologised at the end of the programme to viewers who were offended by his comments and the BBC and Jeremy would like to apologise for any offence caused."
Trade union UNISON has called on the BBC to sack Clarkson, while Prime Minister David Cameron described the star's remarks as "a silly thing to say".