MI5 asked Woolwich murder suspect Michael Adebolajo if he wanted to work for them about six months before the killing, a childhood friend has said.
Abu Nusaybah told BBC Newsnight his friend - one of two men arrested after Drummer Lee Rigby's murder in south-east London on Wednesday - had rejected the approach from the security service.
The BBC could not obtain any confirmation from Whitehall sources.
Abu Nusaybah was arrested at the BBC after giving the interview.
Newsnight reporter Richard Watson said after the interview had concluded he left the studio to find officers from the Metropolitan Police counter terrorism unit waiting to arrest Abu Nusaybah.
The Met confirmed a 31-year-old man had been arrested at 21:30 BST on Friday in relation to suspected terrorism offences and search warrants were being executed at two homes in east London.
The arrest was not directly related to the murder of Drummer Rigby, it said.
The soldier was killed in front of dozens of people near Woolwich Barracks, where he was based, on Wednesday afternoon.
Mr Adebolajo and Michael Adebowale, who was also arrested at the scene, remain in hospital after being shot by police.
In his Newsnight interview, Abu Nusaybah said he thought "a change" had taken place in his friend after a trip to Kenya last year.
He said Mr Adebolajo had told him he travelled there "to study", but instead, was part of a group rounded up by "Kenyan troops" and interrogated in a prison cell.
During his detention he said he was "beaten quite badly", Abu Nusaybah said, and in his opinion, his friend had also been subjected to sexual abuse, although he was too "ashamed" to say exactly what happened.
After this, he became withdrawn "and less talkative - he wasn't his bubbly self", Abu Nusaybah said, adding: "His mind was somewhere else."
He also said Mr Adebolajo was "stopped" upon his return to the UK from Kenya and was later "followed up by MI5" who were "knocking on his door".
He was "basically being harassed", Abu Nusaybah said.
He added: "His wording was, 'They are bugging me - they won't leave me alone.'
"Initially they wanted to ask him if he knew certain individuals.
"But after him saying that he didn't know these individuals, what he said was they asked him if he would be interested in working for them.
"He was explicit in that he refused to work for them but he did confirm he didn't know the individuals."
Reporter Richard Watson said that, in general terms, it was not out of the ordinary for the security service to approach people for information or even to act as covert sources.
Mr Adebolajo, 28, originally from Romford, east London, and fellow suspect Michael Adebowale, 22, of Greenwich, south-east London, had been known to MI5 for eight years, Whitehall sources told the BBC on Thursday.
Two women, aged 29 and 31, arrested on suspicion of conspiracy to murder, have been released without charge, but a man, 29, remains in custody.
Speaking about the fight against the rise of the extremist ideology, Chief Constable of Greater Manchester Police Sir Peter Fahy told the BBC there had been a "steady stream of plots", which had on the whole been foiled by police.
But he said the police and the security services were "particularly concerned" about people travelling from Britain to conflict areas such as Mali, Syria and Iraq and the increase in extremist websites.
Since the murder there has been an sharp increase in the number of in anti-Muslim incidents, according to the organisation Faith Matters, which works to reduce extremism.
Before the attack about four to eight cases a day were reported to its helpline, but the group said more than 150 incidents had been reported in the last few days, including attacks on mosques.
On Friday, Drummer Rigby's wife Rebecca, the mother of his two-year-old son, said she had been aware of the dangers of her husband serving in countries where there was armed conflict, including Afghanistan, but added: "You don't expect it to happen when he's in the UK. You think they're safe."
She said: "I love Lee and always will. I am proud to be his wife. He was a devoted father to our son Jack and we will both miss him terribly."
Drummer Rigby's stepfather, Ian Rigby, said: "We would like to say 'Goodnight Lee, rest in peace our fallen soldier. We love you loads and words cannot describe how loved and sadly missed you will be'."
Mr Rigby added that his stepson "adored and cared a lot for his family, he was very much a family man, looking out for his wife, young son Jack, younger sisters, whom in turn they looked up to him".