The announcement came in a statement from the Foreign Office, which said officials were working with the Libyan Government to deal with it.
It said advice for Britons remains unchanged, and repeated the warning against all but essential travel to the Libyan capital.
A Foreign Office spokeswoman said: "We are aware of reports of a potential threat against the British Embassy in Tripoli and we are liaising closely with the Libyan government.
"There is no change to our travel advice: we still recommend against all but essential travel to Tripoli."
The latest alert comes days after Britons were urged by the Government to leave the Libyan city of Benghazi after it became aware of a "specific and imminent threat".
Britons have also been warned there is a "specific threat" against Westerners in Somaliland.
UK nationals have been advised for some time to stay away from the breakaway territory because of the high threat of criminal and terrorist kidnappings.
The Foreign Office yesterday warned any Britons still remaining in Somaliland that they should leave the country immediately.