The US believes ISIS, through that training, set the stage for the 22-year old to carry out the deadly attack at the Manchester Arena on Monday night, which killed 22 people as they left a pop concert.
Other members of Abedi's family are believed to have been radicalized as well, the official said.
More details are emerging about the British-born killer, who spent time in Libya before the attack and transited through Istanbul and Dusseldorf airports, as police focus on tracking down his associates.
Authorities have made multiple arrests including the bomber's brother, who was detained in Libya.
The latest revelations come as intelligence sharing between the US and the UK resumed
after a temporary halt following a series of high-profile leaks to US media of details surrounding the Manchester bombing investigation, which were blamed on US government officials.
Mark Rowley, assistant commissioner of Britain National Police Chiefs Council, said after receiving "fresh assurances," the UK was now "working closely" its key partners, "including all those in the 'Five Eyes' intelligence alliance."
Under 'Five Eyes,' the US, UK, Canada, Australia and New Zealand share intelligence in one of the world's tightest multilateral arrangements.
US sources were the first to reveal the identity of the bomber, leading to concern that police efforts to hunt down his associates could be impacted.
British Prime Minister Theresa May confronted President Donald Trump about the leaks during their meeting at the NATO headquarters in Brussels on Thursday.
In a written statement, President Trump described the leaks as "deeply troubling" and ordered an investigation. He added that,"There is no relationship we cherish more than the special relationship between the United States and the United Kingdom."
US Secretary of State Rex Tillerson will press the point during his first official visit to the UK on Friday.
Tillerson will meet with British Foreign Secretary Boris Johnson "in an expression of UK-US solidarity following the terrorist attack in Manchester earlier this week," a Foreign Office statement said. The two men will write condolence messages for the victims.
Greater Manchester Police Chief Constable Ian Hopkins told reporters Thursday eight men had been arrested at addresses in Manchester, Wigan and Nuneaton. These arrests are "significant," he said, with searches having "revealed items that we believe are very important to the investigation."
On Thursday, a large cordon was set up for a time around a location in Wigan, where an arrest was made a day earlier, Greater Manchester Police said in a statement.
A raid and search have been ongoing due to the discovery of "potentially suspicious items" and evacuations took place as a "matter of precaution."
Investigators are tracking down associates of Abedi, a British-born national of Libyan descent who was known to intelligence services, saying it is clear they are investigating a network.
A Turkish official said Abedi had transited through Istanbul's Ataturk airport "recently" and did not enter Turkey. The official, who did not want to be named due to government protocol, said he could not confirm where Abedi arrived from or was traveling to. He did say, however, that it could not have been Syria because there are no flights to or from Syria from Istanbul.
The official said Turkey had not received any information from foreign intelligence services about Abedi, so he did not raise any red flags.
Police in Dusseldorf confirmed that Abedi traveled through Dusseldorf Airport in Germany on his way to Manchester a few days before the attack. The suspect was in transit only in the security area.
Abedi 'behaved like a child'
According to a family friend who asked not to be identified, the boys' father had taken his sons to Libya in mid-April and confiscated their passports so they couldn't return to the UK where they'd been in trouble with gangs.
Abedi got his passport back after telling his father he was going on a pilgrimage to Saudi Arabia, but returned to England instead. Abedi was in Libya for three weeks and returned days before his attack, US military officials told CNN.
In Libya, Abedi's brother -- identified as 20-year-old Hashim Ramadan Abu Qassem al-Abedi -- was arrested Tuesday night on suspicion of links to ISIS, according to a statement from a Tripoli militia known as the Special Deterrence Force.
Abdullah Muhsin Norris, chairman of Salaam Community Masjid, a community center in Manchester, told CNN he got into an argument with Abedi in January. Apprently, Abedi wanted to stay after prayers and was wearing his shoes. "Anyway I quarrelled with him and the way he behaved he said I shouldn't shout at him I said, 'I shout at you because you behaved like a child," Norris said.
Armed officers patrol trains
British Transport Police announced Thursday that "specially trained firearms officers will be patrolling on board train services for the first time." It comes after Britain raised the threat level to critical -- the highest in a decade -- and deployed armed soldiers to support police.
"It is important to note that we do not have any specific intelligence in relation to train services but are taking this action to ensure we can protect and reassure the public," BTP Chief Constable Paul Crowther said.
Queen Elizabeth II visited the Manchester Royal Infirmary and Children's Hospital, where some of the wounded are being treated. Speaking to the father of an injured girl by her hospital bed, the Queen said the attack was "a very wicked thing."
Among the 22 victims
were parents, sons, daughters, sisters, brothers, friends, colleagues and classmates. Some were waiting to collect their children, others were enjoying what should have been a fun night of pop music.
A moment of silence was held Thursday morning as the United Kingdom continued to come to terms with its worst terror attack since the 2005 London bombings.
Manchester hospitals are still treating 75 people in the aftermath of Monday's bombing attack, including 23 in critical care, according to a statement from NHS England.