Adebolajo, 28, was asked by the MI5 domestic intelligence agency if he knew certain individuals and later if he wanted to work for them.
But the murder suspect allegedly snubbed the offer, his friend Abu Nusaybah told the BBC, before promptly arrested on the broadcaster’s premises after giving the interview, on suspicion of terrorism offences, the BBC reported.
It is understood the arrest was not directly linked to the brutal murder of 25-year-old soldier Lee Rigby, who was hacked to death in broad daylight Wednesday outside the Royal Artillery Barracks in Woolwich, southeast London.
Scotland Yard police headquarters said counter-terror officers had arrested a 31-year-old man in London on suspicion of the “commission, preparation or instigation of acts of terrorism,” according to AFP.
Adebolajo and Michael Adebowale – the second murder suspect linked with the killing of Drummer Lee Rigby - both remain under armed guard in hospital after being shot by police at the scene, were known to the intelligence services but were reportedly assessed as not posing a deadly threat.
Rigby’s distraught wife said the family found it hard to accept that the 25-year-old had been killed not in a war zone but on the streets of his own country.
A huge pile of floral tributes was building up outside the barracks.
More details emerged about Adebolajo, who was born to devout Nigerian Christians but converted to Islam a decade ago and had attended meetings of the extremist group Al-Muhajiroun, which is now banned in Britain.
He had reportedly sold inflammatory literature at a stall in Woolwich, where his increasingly extremist behaviour in recent weeks had alarmed other Muslims.
Reports said Adebolajo had attempted to travel to Somalia to fight alongside Al-Qaeda-linked Shebab insurgents but had been turned back and had his passport confiscated by police.
Abu Nusaybah told BBC television that Adebolajo had been picked up by Kenyan forces and physically assaulted in detention there.
Shortly after he returned, MI5 agents repeatedly called at his home, the friend alleged.
“His wording was: ‘They are bugging me -- they won’t leave me alone’,” he said.
“After him saying that he didn’t know these individuals and so forth, what he said is they asked him whether he would be interested in working for them.
“He was explicit in that he refused to work for them.”
Adebolajo was captured on film shortly after the attack brandishing a bloodied knife and meat cleaver and claiming he had killed the soldier because British forces killed Muslims every day.
Less is known about the other suspect but he is also believed to be of Nigerian origin.
Dramatic footage of the incident obtained by the Daily Mirror newspaper also showed Adebolajo charging at armed police before he was shot and injured.
Sheikh Omar Bakri Mohammed, the founder of the al-Muhajiroun movement which was banned in Britain under anti-terror laws told Al Arabiya he does “not oppose what [Adebolajo] did.”
“I didn’t teach him to kill, neither did I give him an encouraging or hate-loaded lesson, but it seems that he acted alone,” Bakri said.
Adebolajo came from a Nigerian Christians background converted to Islam a decade ago.
“When someone settles in a non-Muslim country, this means that he is in a peace pact with its people, and both parties should refrain from aggressing one another,” Sheikh Bakri said.
He added that he thinks that Adebolajo decided “to free himself from this peace pact.”
“I am against the method used in killing the victim [Rigby].”