The stab murder bid happened at around 6.20 pm on Tuesday everning, March 6.
The victim, a man in his 20s, sustained life-threatening injuries in the attack.
He was treated at the scene by paramedic crew before being rushed to the emergency department at the Royal Victoria Hospital in west Belfast.
The men – aged 19, 24, and 37 – have been arrested on suspicion of attempted murder and remain in custody, assisting police with their inquiries.
Detective Inspector Michael McDonnell said: “I am appealing to anyone who was in the Great Victoria Street area last night between 6 pm and 6.30 pm and saw anything suspicious, or who has information they believe may be useful to our investigation, to contact detectives at Musgrave on the non-emergency number 101, quoting reference number 1067 of 06/03/18.
“Alternatively information can also be provided anonymously to the independent charity Crimestoppers on 0800 555 111.”