Ismail Abedi is refusing to cooperate with the probe, which is looking at how his two younger brothers, Salman and Hashem, became radicalised and planned their deadly bomb plot.
Abedi, 22, detonated his homemade device in the foyer of the arena at the end of an Ariana Grande concert on 22 May 2017, killing himself and 22 victims as young as eight. Hundreds more people were wounded.
Images from devices recovered at Ismail Abedi’s home during a police raid the day after the bombing indicated he was “sympathetic to the ideals of Isis” (so-called Islamic State), the inquiry has heard.
He was arrested, held for 14 days and interviewed by detectives 25 times, but not charged with any offence, and he denies any involvement.
He had initially refused to give a statement to the inquiry, claiming his legal privilege not to incriminate himself.
Paul Greaney QC, counsel to the inquiry, said that Ismail Abedi, convicted terrorist Abdalraouf Abdallah and Ahmed Taghdi, a friend of the Abedi brothers, had all refused to cooperate. The three deny any knowledge of the bomb plot.
But Mr Greaney he said he now expected they will be served with a legal notice from the inquiry chairman, retired High Court judge Sir John Saunders.
He said the notice would require the attendance of all three at the inquiry to give evidence in person in October.
Mr Greaney outlined a substantial legal to-ing and fro-ing with lawyers for the three men to ask them to provide statements and give evidence.
The counsel said there were “legitimate and important” questions for Ismail Abedi to answer “about the involvement of his brothers in the murders of 22 people”.
The police raid on Ismail Abedi’s home recovered a disk drive containing a number of images that could be “considered supportive of an extremist mindset”, Detective Chief Superintendent Simon Barraclough of Greater Manchester Police told the inquiry last year.
Ismail Abedi told police he had concerns about his younger brothers over their dropping out of their studies.
He denied any knowledge or involvement in their actions or their radicalisation or assistance with the attack, or that he had known or suspected a plot.
Abdalraouf Abdallah denies “grooming” the bomber during prison visits and discussing “martyrdom” with him.
He was released from jail in November on licence after serving a sentence for terror offences, before being recalled in January.
Ahmed Taghdi searched and arranged the urgent purchase of a car, a £230 Nissan Micra used to store bomb-making equipment, the Old Bailey has previously heard. He was arrested but denied any knowledge of the attack and was released without charge.
Hashem Abedi was jailed last year for a minimum of 55 years before parole for his part in the bomb plot.
Lawyers for the victims’ families have condemned the numerous “missed opportunities” by authorities to prevent the attack, from poor staff training and inadequate police patrols to the CCTV blind spot where Salman Abedi hid for almost an hour.
The inquiry was adjourned until Thursday morning.
Additional reporting by PA