The police authorities have previously said they don't believe Abedi had been part of a larger terrorist network, but do think others - with Hashem a suspect - played a hand in planning the attack in Manchester.
British Police have requested that the brother of the Manchester Arena bomber be extradited from Libya in order to arrest him in relation to the murder of the 22 victims killed in the atrocity.
Greater Manchester Police has said it is "engaged with the Libyan authorities and are grateful for them considering the request".
The brothers went to Libya together in April, but only Salman returned.
The militia group said Libya's courts would be able to deal with his case.
In all 512 people were either physically injured or left "profoundly traumatised" Mr Jackson said, with 112 hospitalised.More news: Australia Senate president a dual United Kingdom citizen
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Two people remain in hospital more than five months later.
Prime Minister Theresa May's official spokesman said: "We are determined to do everything in our power to ensure that those suspected of being responsible for the Manchester attack are brought back to face justice in the UK". He targeted concertgoers at Manchester Arena in May.
Its spokesman, Ahmad Ben Salim, told the Reuters news agency: "We will not extradite Hashem Abedi to United Kingdom authorities".
'I want to thank Greater Manchester Police and the Government for their hard work in getting us to this point on behalf of the people of Greater Manchester and all those affected by this appalling act of evil.
However, it now says it is "ready for the next step" if the Libyan attorney general comes to an agreement with British authorities.
Briefing journalists, Greater Manchester Police (GMP) assistant chief constable Russ Jackson confirmed an extradition request for Hashem had been made.