"Historically, and almost philosophically, the US and United Kingdom intel services follow different paths", the official said on condition of anonymity because he wasn't authorized to speak about the investigation.
Victims include an eight-year-old girl and an off-duty police officer.
Almost 1,000 soldiers are being deployed on Britain's streets to support the police.
England's National Health Service said a total of 116 had been injured in the attack, with 75 admitted to hospital.
Queen Elizabeth II visited the Royal Manchester Children's Hospital on Thursday, meeting with staff and some of the attack victims.
Twenty-two people were killed in the explosion at the Manchester Arena.
Grande noted that from the start of her Dangerous Woman tour, she intended for her concerts to be "a safe space for fans", where they could "escape, celebrate [and] heal" - and she said the attack wouldn't change that.
"That incident stirred up a sense of anger among young Libyans in Manchester and especially Salman, who clearly expressed his desire for revenge", said the source, declining to be named.More news: Attack On Coptic Christians Kills At Least 24 In Egypt
Ms May said a new attack "may be imminent" and stressed that the soldiers would remain under police command.
Another sibling, 18-year-old brother Hashim, and Abedi's father were arrested in Tripoli on Wednesday.
The leak of his name put the investigation at serious risk, because it alerted Abedi's family and associates that the police were on to them before raids could be arranged, which meant they could potentially escape from police and the army.
The pictures published by the New York Times included remains of the bomb and of the rucksack carried by the suicide bomber, and showed blood stains amid the wreckage.
Hours before the attack, he had phoned his mother and said "forgive me", according to a Libyan anti-terror official. He criticised media for publishing such material."Who's leaking it?"
The revelation came from a leaked transcript of an April 29 phone call between the two leaders.
"People talk about the planning and the intelligence you need to plan an attack". "We will continue to collaborate and work together to ensure we do everything we can to keep citizens and communities safe".
The official said Turkey had not received any information from foreign intelligence services about Abedi, so he did not raise any red flags.
USA channel ABC News reported that police had found a kind of bomb-making workshop in Abedi's home and he had apparently stockpiled enough chemicals to make additional bombs. The report also suggested that the bomb was an improvised device made with forethought and care.