A second police source said none of the men were offenders who would be well known to the public.
He did not recognise the names when told who the men were by colleagues and said they were "certainly not" among the country's best known criminals from the prison's notorious D block.
These inmates include murderers William Bell, Graeme Burton and Liam Reid.
Police were called to the prison just after the attack at 10am when three men attacked another in a cell. The fight spilled on to a landing area outside the cell and a second inmate was assaulted.
"Both victims received a beating and were stabbed with home-made weapons," a police spokesperson said. additional reporting: Natalie Akoorie