The UK's Crown Prosecution Service (CPS) has put in a formal request for extradition of Hashem Abedi, the younger brother of Salman Abedi, who also died in the explosion at Manchester Arena.
Hashem is wanted by authorities for the murder of 22 people and the attempted murder of over 500 others, who were injured and conspiracy to cause an explosion, Greater Manchester Police (GMP) said in a statement.
"Hashem Abedi is currently detained in Libya and the CPS has now requested that Libyan authorities consider his extradition back to the United Kingdom.
He said that the police force has been working with "considerable speed" with officers drawn from across UK policing to support it.
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The police now have a clear understanding of Salman Abebi's movements but believe until they are able to interview Hashem, the details remain incomplete.
He was held in Tripoli by members of the Rada Special Deterrence Force a day after the attack on May 22 and the Libyan authorities are believed to be aware he was still alive.
"This investigation is still running at a very fast pace. We are incredibly grateful for the support of the hundreds of people affected by this horrible attack and our officers are constantly moved by their stories and by their accounts," Jackson added.
A total of 112 people needed hospital treatment after the attack, with 64 suffering "very serious" injuries.
Physical injuries include paralysis, loss of limbs, internal injuries and very serious facial injuries.
Many have had complicated plastic surgery.
Two people remain in hospital more than five months later.
Salman Abedi was 16 when he first visited Libya, the country his parents fled in 1993 to escape persecution under Colonel Gaddafi.
Manchester police is examining more than 16,000 hours of CCTV footage and working through 8 million lines of telephone communications data.