Abu Nusaybah went on to say that Adebolajo appeared changed and withdrawn after his return from Kenya.
The pair first met in 2002, he said. Abu Nusaybah had converted to Islam in late 2004 and Adebolajo followed suit about four months later, he said.
A security source told CNN that "we would never comment" on the kind of allegations made in the interview.
London's Metropolitan Police Service said a 31-year-old man had been arrested in London on Friday night on terrorism-related offenses, but following standard practice, would not give the arrested man's name.
Officers from Counter Terrorism Command arrested the man under the Terrorism Act, on suspicion of the commission, preparation or instigation of acts of terrorism. He was taken to a south London police station, where he remains in custody, a police statement said.
Search warrants were being executed at two homes in east London, police said.
Kenyan counterterrorism sources told CNN on Saturday that Adebolajo traveled to Kenya in November 2010 and was arrested in the coastal town of Lamu for trying to cross illegally into Somalia.
A spokesman for the Kenyan government said Sunday that Adebolajo used the name Michael Olemindis Ndemolajo when he was arrested and taken to a court in Mombasa.
Kenyan officials turned him over to British authorities in Kenya when they discovered he was a British citizen, Muthui Kariuki said.
"He was interrogated by British security officials," he said.
Lamu is part of an area near the Somali border that has been the stage for attacks by armed gangs and suspected operatives from the al Qaeda-linked Al-Shabaab militant group.
No charges were filed against Adebolajo, according to the Kenyan media.
The British Foreign Office said: "We can confirm a British national was arrested in Kenya in 2010. (We) provided consular assistance as normal for British nationals."
It's not clear whether Adebolajo may have traveled to the region on more than one occasion.
CNN understands that one line of inquiry being examined in the Woolwich terror investigation is that Adebolajo might have attempted -- but failed -- to travel to Somalia some time last year.
Al-Muhajiroun connections claimed
A self-proclaimed former radical associate of Abu Nusaybah told CNN terrorism analyst Paul Cruickshank he had been a follower of the group Al-Muhajiroun, a British group of Islamic extremists virulently opposed to UK intervention in Iraq and openly supportive of al Qaeda.
The former associate -- who spoke to CNN on condition of not being named -- spent time with Abu Nusaybah in Al-Muhajiroun study groups in Luton, a town north of London, in the years leading up to the July 7, 2005, attacks on London's transit system, he said.
At the time, Adebolajo himself was a follower of the group and attended meetings in London, according to several Al-Muhajiroun insiders, before moving away from the group two or three years ago.
"Abu Nusaybah was very quiet, always smiling, and very religious," said his former friend, who has now shed his radical views.
He said their circle of friends in Luton included Taimour Abdulwahab al Abdaly, who carried out a suicide bombing in Stockholm in December 2010 in which he was the only fatality.
He said Abu Nusaybah had connections to a group of Somali extremists in Luton.
It is understood that the two individuals suspected in the knife and cleaver attack were known to Britain's domestic security service. They had featured in previous investigations into other individuals, but were not themselves under surveillance.