Lord Hall is reported to have received a threatening email after dropping presenter Jeremy Clarkson from Top Gear because he had punched a producer.
The Mail on Sunday also reported Lord Hall and his wife were under 24-hour protection from security guards at their Oxfordshire home.
The Met said the email appeared to have been sent from outside the UK.
"Police in Westminster are investigating an allegation of threats to kill," a Met spokesman said.
"The allegation was reported to police on Wednesday, 25 March.  The threat was made by email."
He said inquiries were continuing to establish from where the email was sent.
No arrests have been made.
A BBC spokeswoman said: "We wouldn't comment on security matters."
Lord Hall announced his decision not to renew Clarkson's contract on Wednesday - after an internal inquiry found the presenter had subjected producer Oisin Tymon to an "unprovoked physical and verbal attack" at a North Yorkshire hotel.
Mr Tymon, who suffered a split lip, did not file a formal complaint and it is understood Clarkson reported himself to BBC bosses following the incident, and was suspended.
The row - which took place on 4 March - was said to have occurred because no hot food was provided following a day's filming.
Lord Hall said he had not taken his decision lightly, but insisted "a line has been crossed".
More than a million people signed an online petition to reinstate Clarkson.
The Mail claimed the death threats were made to Lord Hall via email the same day as his announcement.
It also published photographs of security guards outside his home.
Mr Tymon, who previously described Clarkson as a "unique talent", has himself come under sustained abuse on social media for his involvement in the dispute.
Speaking outside his home on Thursday, Clarkson asked fans to show restraint.
Alleged death threats made against BBC director general Tony Hall are being investigated by the Met Police.