Two sources familiar with the investigation told Reuters authorities were investigating a possible link to Nigeria.
The British soldier was hacked to death by suspected Islamists, while two men remain under arrest in hospital.
BBC says the soldier’s family had been informed.
Prime Minister David Cameron convened an emergency meeting of his intelligence chiefs on Thursday to look at the incident.
A dramatic clip filmed by an onlooker just minutes after Wednesday’s killing showed a man with hands covered in blood shouting Islamic slogans and promising revenge on Britain for its participation in wars in the Muslim world.
“We swear by almighty Allah we will never stop fighting you. The only reason we have done this is because Muslims are dying every day,” the black man in his 20s or 30s, wearing a wool jacket and jeans and speaking with a local accent, shouted in the footage obtained by Britain’s ITV news channel.
“This British soldier is an eye for an eye, a tooth for a tooth.”
The attack, just a month after the bomb attacks on the Boston Marathon and the first apparent Islamist killing in London since suicide bombers struck in July 2005, revived fears of so-called “lone wolves” who might have had no direct contact with al Qaeda.
Chilling images of a blood-soaked killer urging Britons to overthrow their government or risk having their children face a fate similar to a dead soldier lying just yards away were splashed across the front pages of newspapers.
Police shot the two suspects while trying to arrest them, and the wounded men were taken into custody.