Suicide bomber Salman Abedi killed 22 – including children – and injured 64 outside an Ariana Grande gig.
The UK terror threat level is now at its highest level of “critical”, meaning more attacks may be imminent.
In Libya, the bomber’s father, Ramadan, and younger brother, Hashem, have been arrested, Reuters is reporting.
Hashem, 20, was reportedly arrested in the capital Tripoli on suspicion of links with so-called Islamic State, according to Reuters.
Older brother, Ismael, was detained in Chorlton, south Manchester, on Tuesday.
Their father was in Tripoli when he was arrested, Reuters has told the BBC.
In Wigan, police said the arrested man had been carrying a package which is now being “assessed”.
Eyewitness Connor Britton told the BBC the man had been held by “undercover armed police”.
He said workers in his office had been told to stay inside and lock their windows, and that a red package had been “moved to a clear part of the street”.
Meanwhile, military personnel are being deployed to protect key sites after the terror threat level was raised.
Salman Abedi is understood to be a 22-year-old born in Manchester to Libyan parents, and a former University of Salford student.
He attended Burnage Academy for Boys in Manchester between 2009-11, and The Manchester College until 2013.
Hamid El-Said, who worked for the UN on tackling radicalisation and now works at Manchester Metropolitan University, said Abedi had a “really bad relationship” with his family and his parents had tried but failed to keep him on the “right path”.
“Eventually he was doing very bad at his university, at his education, and he didn’t complete, and they tried to take him back to Libya several times. He had difficulties adjusting to European lifestyle,” he said.
A former classmate of Abedi’s told the BBC that he was a “very jokey lad” but also “very short tempered” and would get angry at “the littlest thing”.
The man, who did not want to be identified, said Abedi was “away at random times throughout the year”.
He did not know if Abedi was abroad or playing truant because he hung around “the wrong crowd and was very, very gullible”.
The man said that, before leaving the school in 2011, Abedi became “more and more religious” and that this might explain why he cut ties with former classmates.