Manchester police has said, according to local media, that one of the men was arrested following a property search in the Withington area of Manchester, while another was detained elsewhere in the city.
The singer has not yet spoken publicly about the Monday night blast that killed at least 22 people and left dozens injured.
The father had earlier said his son was innocent.
The father and brother of the Manchester Arena bomber have been arrested in Libya's capital Tripoli.
"I think it's very clear that this is a network that we are investigating", police chief Ian Hopkins said outside Manchester police headquarters.
Authorities believe he had help in building the bomb, which photographs published by the New York Times showed was sophisticated and powerful, and that his accomplices could be ready to strike again.
British officials said a 23-year-old man was arrested in South Manchester in connection with the attack, but did not divulge further details about that individual's identity.
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British Prime Minister Theresa May will raise the issue with U.S. President Donald Trump when she meets him at a North Atlantic Treaty Organisation summit in Brussels later on Thursday, a government source told Reuters.
Flowers laid beneath Cobden statue in St Ann's Square in Manchester to mourn victims of the bomb attack.
After Trump defended his decision to discuss intelligence with the Russians during a White House meeting, May said last week that Britain would continue to share intelligence with the United States.
Asked if he was known to the intelligence services, she said: "The security services will know a lot of people, it doesn't mean they are expected to arrest everybody that they know but it is somebody that they had known before and I'm sure when this invetigation concludes we'll be able to find out more".
The issue of the leaks will be raised at the very highest level when the Prime Minister and the US President will meet to discuss, amongst other things, counter-terrorism.
But with just over two weeks to go until a national election, May's Conservatives and political parties said they would resume campaigning in the coming days.
Late Wednesday, the Greater Manchester Policy named two more teenagers killed in the attack - Chloe Rutherford, 17, and Liam Curry, 19.