Det Chief Insp Jude Ashmore said more witnesses had come forward after police made an appeal on Monday following the death of 21-year-old Kavan Brissett.
Mr Brissett was stabbed in an alleyway on Langsett Walk, Upperthorpe, at around 6.45pm on Tuesday, August 14. He was taken to the Northern General Hospital where he died on Saturday, August 18.
Det Chief Insp Ashmore said: "Intelligence and information is now coming into our major incident room at a good pace and I’d like to thank everyone who has come forward so far.
“There are of course, still more people we need to speak to. Someone, or several people out there know what happened to Kavan and know who is responsible for his death.
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"I’d like to ask those people to think about Kavan and his family, who have been robbed of a life with their loved one. We need people to keep talking to us so we can provide answers for them.”
Chief Supt Stuart Barton, Sheffield's district commander, said there were people in the street just before the incident.
DCI Ashmore said: “Our efforts to piece together Kavan’s movements prior to his death continue and we know that he was with members of his family about an hour before. It’s that hour gap that we need more information on so we can understand where he went and what he was doing which resulted in him being on Langsett Walk last Tuesday evening.
“There were a number of people in the street when Kavan was injured, many of who tried to help him and called for an ambulance. We’ve already spoken to most of these people but we believe there are still some who have not yet come forward. If you were there and saw what happened, please get in touch with us.
“So far, in addition to speaking to witnesses, we’ve carried out extensive house to house enquiries in the area, conducted a CCTV trawl, telephone work and gathered intelligence from the local community. This work will continue as the investigation progresses and reassurance patrols will also continue throughout the week.
“Kavan was a young man who had his whole life ahead of him. He enjoyed keeping fit and going to the gym and had recently completed a fitness qualification.
“His family have been left utterly devastated by his death and we are doing everything we can to support them and to get answers for them. When Kavan was taken to hospital, he remained critically ill for a number of days.
"His family were by his side every single day and were left heartbroken when the decision was made by the hospital to turn off his life-support machine.
“I’d ask anyone who has information and who hasn’t yet come forward to keep Kavan and his family at the forefront of your mind, we’re doing this to provide answers for them and to get justice.
“You can speak to detectives directly by calling our incident room on 01709 443458 or via 101, quoting incident number 827 of 14 August 2018. People can also Crimestoppers, anonymously, on 0800 555111.”