The 26-year-old injured man was found with a head wound near a stairwell on Fitzalan Square next to William Hill bookmakers.
He was taken to hospital where police later received reports on the incident. Officers spent the day carrying out enquiries and a police spokesman said the incident is an ‘ongoing investigation’.
Reports on social media claimed the injured man was assaulted.
An eye-witness said he saw officers attend Fitzalan Square earlier this morning to seal off a stairwell next to William Hill bookmakers which meets Pond Street.
Crime scene investigation officers were seen taking pictures of the scene this afternoon as they gathered up evidence.
A South Yorkshire Police spokesman said: “A 26-year-old man was taken to Northern General Hospital after being found with a head injury at around 4.25am this morning. He remains in hospital at this time.
“Police are still carrying out enquiries to try and establish how the man came to receive his injuries.”
Anyone with any information is being urged to contact 101.
UPDATE: Police have issued an appeal about the incident.
“Detectives would urge you to please come forward as a man is currently in a life-threatening condition in hospital after he was found unconscious and with serious injuries close to Fitzalan Square.
“The 28-year-old man was discovered at the bottom of one flight of concrete stairs leading off the Square and down towards Pond Street at around 4.25am. He was immediately taken to hospital where he remains critically ill with a serious head injury.”
Detective Sergeant Iain Rawlins investigating said: “We are trying to ascertain the exact circumstances of this incident and I would urge anyone who may have been in the Fitzalan Square area to please make contact with us.
“Even if you don’t believe you have any information, or you think the details you have may not be useful, it could prove to be vital to our investigation and to establishing exactly what happened to the man and the nature of how he sustained his injuries.”
Please call 101, or Crimestoppers anonymously on 0800 555111, quoting incident number 128 of 7 June 2016.