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.
The Met Police said 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 his detention by security forces on a trip to Kenya last year.
Abu Nusaybah said Mr. Adebolajo suggested he had been physically and sexually abused during an interrogation in a prison cell in the African country.