One of the men was detained following searches of an address in the Withington area of the city, while another was arrested in a part of Greater Manchester that was not disclosed.
Jomana Abedi said the 22-year-old called his mother moments before detonating a nail bomb in the foyer of Manchester Arena following an Ariana Grande concert, killing 22 people and injuring scores more.
Using freakish failed logic, Jomana said her terrorist brother was angry at "explosives America drops on children in Syria".
Her only direct comment since the attack has been a social media posting shortly afterwards in which she said she felt "broken" and "so so sorry".
But members of the Libyan immigrant community reported to local authorities that they feared Salman was turning increasingly radical, two friends of the family said.
Police said relatives of all those killed had been informed and specialist officers were supporting them.
Initial analysis of the various elements photographed at the scene suggests that suicide bomber Salman Abedi carried "an improvised device made with forethought and care", concealed most likely within a backpack but also possibly in a vest, wrote the paper.
Investigators have said they are now looking at Abedi as part of a larger terrorist network that extends outside of Britain, though his father says that his son was not a jihadist.
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In a Facebook post, the Special Deterrence Forces, which operates out of a former United States military base, said that Hashem had been an ISIS member, had been involved with the Manchester plot, and was en route to withdrawing 4,500 Libyan dinars (about US$560) sent by Salman when he was arrested Tuesday night by the militia. His 20-year-old brother Hashem was arrested in Libya late Tuesday night by the Special Deterrence Forces, according to officials there.
Multiple UK media reports are reporting that Greater Manchester Police has suspended the sharing of information relating to the Manchester attack with USA officials.
Authorities in Britain have become increasingly angered by USA leaks from the investigation, including the bomber's name on Tuesday and the photos of blood-stained fragments from the bomb on Wednesday. The terror attack had already led to the UK's political parties suspending general election campaigning, with polling day just over two weeks away on June 8.
A relative of the Manchester bomber warned the British authorities that he was "dangerous", according to claims in The Times.
Chief Constable Ian Hopkins of the Greater Manchester Police said on Wednesday, "This is clearly a network that we are investigating, and extensive activity is taking place across Greater Manchester as we speak".
The BBC reported that security services thought the bomb was too sophisticated for Abedi to have built by himself.
In total, eight men, including Abedi's older brother, and a woman have been arrested in a series of raids across Manchester, Wigan and Nuneaton.
The news has yet to be confirmed by Ariana or her team, but the report comes after the brunette beauty said she was left "broken" by the tragic events. "I know everything about my brother, what he was doing there in Manchester".
The attack killed 22 people, all of whom have now been identified by police but their names will be released during the course of this week after formal identifications are complete.