In the interview with BBC's "Newsnight," Abu Nusaybah said MI5 had approached Adebolajo in the past year, asking if he wanted to work for them.
Adebolajo rejected the approach, according to his friend.
Abu Nusaybah said the contact from MI5 occurred last year after Adebolajo returned from a visit to Kenya during which he was detained by security forces.
Adebolajo told his friend that he was physically assaulted and sexually threatened during his detention.
CNN is working to independently verify the allegations made by Abu Nusaybah about his friend's treatment in detention.
Abu Nusaybah went on to say that Adebolajo appeared changed and withdrawn after his return from Kenya.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.