Kavan Brissett, aged 22, was knifed in his chest in an attack off Langsett Walk, near Upperthorpe, on Tuesday, August 14.
He underwent emergency surgery but died in hospital four days later when his life support machine was switched off.
Detectives are treating the stabbing as a targeted attack.
Detective Chief Inspector Jude Ashmore, who is leading the police probe into the murder, said detectives are committed to cracking the case for Kavan’s family and friends.
“We have a team working on this every single day. Even when other incidents occur, other murders, this does not stop. There’s a dedicated team of detectives working on this investigation,” she said.
She said a ‘key strand’ of the investigation is the search for Ahmed Farrah, 29, who is believed to hold vital information about the killing.
Farrah, who has links to Broomhall and is also known as Reggie, is said to know he is wanted and is accused of deliberately evading arrest.
DCI Ashmore said detectives have travelled to other parts of the country in search of the fugitive.
They have also tracked down friends, relatives and acquaintances and served a number of official notices warning people that they risk prosecution if they are found to have been assisting an offender.
DCI Ashmore said detectives are also working hard on reviewing and enhancing CCTV footage and analysing mobile phone use.
“Kavan was in the area on the day in the company of others when this occurred. We are working on accounting for his movements throughout the day, which also relies upon witnesses, members of the public, CCTV and telephone work. We are piecing it all together,” she said.
A £5,000 Crimestoppers reward for information leading to Farrah’s arrest has been extended and is now available until April.
DCI Ashmore added: “It is really important that we get justice for Kavan.
“All those who knew him said he was a really lovely lad. His death has affected a lot of people.”
Anyone with information should call South Yorkshire Police on 101 and quote incident number 827 of August 14.
Crimestoppers can also be contacted, anonymously, on 0800 555111.