The Daily Telegraph reported that the star would be dropped after an internal investigation concluded he had attacked a producer on the show.
It said director general Tony Hall would explain that such behaviour could not be tolerated at the BBC.
Clarkson tweeted a rebuttal of the story on Wednesday morning.
"Just to keep everyone up to date, I haven't heard a thing," he wrote, shortly before 10:00 GMT.
The BBC also says no final decision had been made on Clarkson's future.
"When we have an outcome, we will announce it," said a BBC spokesman.
Clarkson was suspended 16 days ago following an alleged "fracas" with producer Oisin Tymon.
The row was said to have occurred because no hot food was laid on for the presenter following a day's filming in North Yorkshire.
An internal investigation began last week, led by Ken MacQuarrie, the director of BBC Scotland.
Mr Tymon did not file a formal complaint and it is understood Clarkson reported himself to BBC bosses.
The BBC's director of television, Danny Cohen, felt he had no choice but to suspend the presenter pending an investigation.
The decision caused an outpouring of support from Top Gear fans, with more than a million people signing an online petition to reinstate him.
Whatever the outcome of the BBC's inquiry, the motoring show is expected to continue.
It is one of BBC Two's most popular programmes, and overseas sales generate an estimated £50m a year for the corporation's commercial arm, BBC Worldwide.
Whether Clarkson's co-presenters James May and Richard Hammond would continue in his absence has yet to be confirmed.
All three have their contracts up for renewal this year.
Meanwhile Radio 2 DJ Chris Evans, who has been touted as a potential replacement for Clarkson, has ruled himself out of the running.
"Not only is it not true, it's absolute nonsense," he told listeners on Wednesday morning.
"From what I've seen on Twitter and various social media, there's a 50/50 split approximately as to whether me being involved in the show is a good idea.
"In TV or radio, if you get a 50/50 love/hate reaction that usually equals massive hit. I used to work for [ratings body] Barb and knock on people's doors and this was the rule of thumb.
"However, I'm in the no camp. So regardless of whether it would be a hit, I'm voting a no for myself on that show, so that's never going happen.
"And that's the end of that."
Speaking later to reporters outside Radio 2, Evans refused to speculate on who else might replace Clarkson, saying he "doesn't know if the post is available yet".

However Rami Jarrah said in his post that his detention appeared to be related to his work in Syria.
His arrest caused concern among media groups, who called for his release.
Jarrah - who met Turkish President Recep Tayyip Erdogan in January - was held in the city of Gaziantep.
He was reported to be applying for a residence permit at the time.
"The location I was transferred to late Wednesday evening contained prisoners that were all held under the same suspicion of being terrorist elements, all have not been charged and some have been there for up to nine months after having being declared innocent by a court of law," Mr Jarrah said in his Facebook post.
"It disturbs me that I was placed in this situation given my background and obvious distance from such an accusation."
The reporter said that while he understood "the pressure the Turkish government is under" and the responsibility it has to prevent terrorism, a little more research by the authorities would have prevented unnecessary hardship.
The Committee to Protect Journalists said at the time of his arrest that Syrian journalists should be protected rather than detained.
Jarrah founded the independent citizen journalist group Ana Press, providing reports to international media, after leaving Syria.
He was initially held in a detention facility for foreign citizens, but was moved to a different facility on Thursday, the CPJ said.
Supporters say Jarrah is well known for his independent reporting, often carried out at great personal risk.
Jarrah, who was brought up in the UK, fled Syria with his wife and child in 2011, fearing that he was in danger, but continued to go back to report.
Press freedom 'a major concern'
Turkey urged to free Syrian journalist
Top Gear presenter Jeremy Clarkson says he "hasn't heard a thing", after press reports suggested the BBC would sack him on Wednesday.
[NEXT_CONCEPT]
A Syrian journalist who was arrested on Wednesday in Turkey has been released without charge and with no explanation as to why he was detained, he announced on Facebook.