The man is the 18th person who has been arrested during the investigation into the terror attack, which killed 22 people including children.
The source told the Telegraph: "The suspicion is that these guys were also part of the plot and either knew about it beforehand or were actively encouraging Abedi to carry out the attack".
Libyan authorities took Abedi's father and younger brother into custody.
The insider added: "They indoctrinate teenagers at this school and then the terrorist recruiters take their pick".More news: United Kingdom police fire 50 shots to stop London attack
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The Battar unit was formerly located in Syria, but several of the fighters relocated to Libya, as Libya is the country from where they originally hailed.
British security forces believe he was radicalised in Manchester, and that he worked alone in committing his atrocity. Abedi maintained this contact, even as he returned back to Manchester, although he employed some security precautions, such as using disposable phones or receiving the messages indirectly from another friend in Germany or Belgium.
The latest man was detained on suspicion of offences contrary to the Terrorism Act.
Five people from the North East were among the 22 who died in the suicide bomb attack in Manchester Arena; Chloe Rutherford, 17, and boyfriend Liam Curry, 19, from South Shields; Hartlepool born Jane Tweddle-Taylor, 51; and Philip Tron, 32, and his partner's daughter Courtney Boyle, 19, from Gateshead. Six people, including two cousins of attacker Salman Abedi, pictured, have been released without charge.