The 19-year-old man was arrested yesterday in a raid on the former home of Abedi.
The police statement said one of the last places he went to before the attack at the Manchester Arena venue was a city centre flat, where they believe he may have finished assembling the device.
The source told Reuters that Abedi was not among the 3,000 people now under active investigation by MI5, although he was one of about 20,000 people known to the agency, which focuses on countering terrorism and espionage.
A 23-year-old man was arrested in Shoreham-by-Sea, some 400 kilometers (250 miles) from Manchester, "on suspicion on offences contrary to the terrorism act", Greater Manchester Police said on Twitter Monday morning.
It was while at Manchester College that two people who knew Abedi have confirmed they made separate calls to an anti-terrorism hotline to warn the police about his extremist views.
Police raided more homes on Monday as the relentless search for the network behind the suicide bombing continued a week on from the attack.
Sussex Police is asking communities to stay alert but not be alarmed following the arrest of a man in in connection with the terror attack in Manchester.
MI5 will look at any assumptions that were made prior to the bombing last Monday, which killed 22 people and injured 116.
Abedi was known to British security services before the bombing, the government has said, but Rudd declined to comment on exactly what had been known about him. More than 20 people were killed in an explosion following a Ariana Grande concert at the Manchester Arena late Monday evening.
British authorities say they have disrupted five plots since March 22, when a terror attack outside Parliament in London left five people dead. His elder brother Ismail is among the suspects being held in Britain, and a younger brother and Abedi's father have been detained in Libya.
On Sunday, police released photographs from security cameras showing Abedi on the night of the massacre, wearing jeans and trainers, a black bodywarmer and a baseball cap, with the straps of his backpack visible on his shoulders.
Officers released CCTV pictures of Abedi on the night of the attack and want members of the public to help them track his movements after he returned to Britain on 18 May - reportedly from his family's native Libya.
Britain has downgraded its national security level from its highest level.
The terror threat level now indicates that an attack remains highly likely rather than imminent.