He said MI5 agents approached Adebolajo after he returned to Britain and initially asked him if he had met specific Muslim militants, then asked Adebolajo if he was willing to act as an informer.
"He was explicit in that he refused to work for them," Nusaybah said.
The BBC said police arrested Nusaybah outside its studios Friday night immediately after recording the interview.
"This interviewee had important background information that sheds light on this horrific event," the BBC said in a statement. "And when we asked him to appear and interviewed him, we were not aware he was wanted for questioning by the police."
London police confirmed that a 31-year-old man was arrested Friday night on suspicion of "the commission, preparation or instigation of acts of terrorism." Police declined to identify Nusaybah by name or provide further detail.
It was not immediately possible to verify the information provided by Nusaybah, who said he had known Adebolajo for about a decade. MI5 does not publicly discuss its efforts to recruit informers.
It is not uncommon, however, for special services officers to occasionally visit communities to ask people if they know potential terror suspects or others under MI5 surveillance.
Potential informants go through a screening process to determine if they should be trusted, what their motivation might be and whether their information would be likely to be accurate.
Nusaybah said Adebolajo was converted to Islam around 2004. His account corroborates those provided by two Muslim hard-liners who said they also knew Adebolajo.
Anjem Choudary, a former leader of a banned British radical group called al-Muhajiroun, said Adebolajo was a Christian who converted to Islam around 2003. Choudary told The Associated Press that Adebolajo participated in several of the group's London demonstrations before Britain outlawed the group in 2010.