Clarkson Row: BBC Boss 'Sent Death Threats'
Lord Hall, 64, and his wife Cynthia have been under 24-hour guard at theirÂ OxfordshireÂ home since the threats were made on Wednesday, according to reports.
"Police in Westminster are investigating an allegation of threats to kill. The allegation was reported to police on Wednesday, 25 March.
"The threat was made by email.
"Enquiries continue to establish from where the email was sent, although the content of the message suggests from outside the UK."
A BBC spokeswoman said: "We wouldn't comment on security matters."
Lord Hall, former chief executive of the Royal Opera House, took over the ÂŁ450,000 BBC post in April 2013, replacing George Entwistle, who left the corporation in the wake of the Jimmy Savile sex abuse scandal.
He announced on Wednesday that Clarkson would not be retained on the motoring show, saying "a line has been crossed"Â after the unprovoked attack on producer OisinÂ Tymon.
He added that "there cannot be one rule for one and one rule for another".
Mr Tymon had his lip split by Clarkson in a 30-second-long assault on 4 March and took himself to hospital with his injuries.
He was also shouted at by the former Top Gear presenter in a torrent of verbal abuse over food at a hotel in North Yorkshire.
Clarkson reported the incident to the BBC five days later and was suspended by the broadcaster on 10 March.
On Friday, Mr Tymon, who has himself received death threats and abuse from trolls on Twitter, said he did not want to press charges against his former colleague.
North Yorkshire Police said the force is still investigating the incident.Â
Police could yet bring a charge against 54-year-old Clarkson, although it appears any prosecution would be without the support of the victim himself.
Meanwhile, it remains unclear as to who will take over at Top Gear.
Chris Evans leads the betting as favourite to take over the show, even though he has ruled himself out on more than one occasion.
Top Gear co-hosts James May, 52, and Richard Hammond, 45, have not announced if they will stay at the show or not, but have heavily hinted that they will follow Clarkson out of the corporation.
Asked earlier in the week if he will continue on the BBC2 show, May said the trio came "as a package" and his future requires "a lot of careful thought".