More than 800,000 people signed a petition demanding he keep his job after he was suspended following the fracas with producer Oisin Tymon which was sparked when Clarkson was told he could not have a £21.95 (€30) hot steak.
Clarkson told BBC News: “I am very grateful to everybody.” He is expected to comment on the incident in his column in The Sun today but it could be weeks until his fate is decided by an internal disciplinary inquiry.
It is understood not all the potential witnesses to the row have yet been contacted ahead of the hearing.
The programme’s stars — Clarkson and co-hosts James May and Richard Hammond — are scheduled to appear at four live shows in Norway on March 27 and 28 and a decision on whether to go ahead is expected early next week.
All three men’s contracts expire three days after the Norway gigs, which could render any disciplinary hearings redundant.
The last three episodes of the series have currently been put on hold.
The process was begun by Clarkson, who told bosses at the BBC about the row which led to his suspension.
A family who witnessed the row said Clarkson was staying at the Simonstone Hall Hotel in North Yorkshire and went into the bar at around 9.30pm after a day of filming last Wednesday.
Bob Ward, 60, from Leeds, told Sky News the star refused to have a selfie taken with him, saying: “No, not with the day I have had.”
His wife Sue claimed Clarkson then said it was “ridiculous there was nothing to eat” and she said he thought his colleague had not done his job properly.
“Obviously there were lots of expletives in between all this,” she added. She said Clarkson told his colleague “he would see to it that he would be losing his job”.
The fracas was described as just “pushing and shoving” by a source in The Sun.
The Top Gear star has attracted high-profile support, with David Cameron calling him a “huge talent” and saying he hoped the situation could be resolved so his children would not be left “heartbroken”.
BBC director-general Tony Hall has also said he was a “fan” of Clarkson, but added that allegations of a fracas were “serious”.
The BBC disciplinary panel will be led by Ken MacQuarrie, the head of BBC Scotland.
A lawyer for Mr Tymon said his client “intends to await the outcome of the BBC investigation and will make no comment until that investigation is complete”.