Inquest hearings will be held in due course, and any final decision about his remains will be down to a coroner.
His body has never been kept in the same place as his 22 victims, the source told the men.
Abedi's family cannot receive his body as his parents Ramadan and Samia as well as younger brother Hashem, 20, are in Libya.
His father and younger brother are still in detention in the country. Detectives said Hashem had links to ISIS and was planning to carry out a terror attack in Tripoli.
His elder brother, Ismail, 24, remains in custody in Manchester.
The revelations come as counter-terrorism police said last night that Salman may have acted alone.
In the four days between travelling to the UK from Libya and carrying out the atrocity that killed 22 people, he bought most of the components and built the bomb by himself, they said.
Police said they could not rule out that the Libyan was part of a wider network, but after seven days of investigation involving 1000 officers and "hundreds" of witnesses, they concluded that he mostly acted alone.
This runs counter to the impression given so far in the investigation, which has seen 16 arrests.
Last night three suspects, aged 20, 24 and 37, were released without charge.
Officers said a blue suitcase Abedi was seen with hours before he launched the attack remains a focus of their inquiry.
It may contain crucial evidence that could allow forensic experts to piece together the gaps in his final movements.
Although detectives have no reason to believe the bag contains anything dangerous, they are warning the public not to approach it, and instead call 999 immediately.
Detective Chief Superintendent Russ Jackson, head of the North West Counter Terrorism Unit, said: "Our enquiries show Abedi himself made most of the purchases of the core components. Many of his movements and actions have been carried out alone during the four days from him landing in the country and committing this awful attack.
"It is vital that we make sure that he is not part of a wider network and we cannot rule this out yet. There remain a number of things that concern us."
Abedi had a "relatively minor" criminal record as a teenager but was not known to police for holding extremist views.
He appeared on police logs in 2012 over offences of theft, receiving stolen goods and assault, Greater Manchester Police chief constable Ian Hopkins said.
However, Abedi had not featured in Prevent, the Government's voluntary counter-radicalisation scheme.
Hopkins also said charges of conspiracy to murder could be brought as a result of the huge investigation into Abedi's suspected network.