Police are searching for Sean Bulle, aged 20, over the murder which happened in Heath Town just before 5.20pm on Monday.
A man, also aged in his 20s, was stabbed to death with a machete outside a block of flats in Chervil Rise.
Detectives say they have followed a a number of lines of enquiry to track Bulle down but have so far been unable to track him down.
Detective Inspector Jim Mahon, who is leading the murder probe, warned the public against approaching Bulle and said that anyone considering helping him risked being prosecuted.
He said: "We have been working hard to establish what happened yesterday afternoon and are following up a number of lines of enquiry.
“We believe Bulle may have been involved and I am asking for your help in tracing him.
“If anyone knows where he is or thinks they may have seen him, I would urge them to our incident room on 101, extension 861 3026 immediately.
“Anyone who may be shielding him through a sense of misguided loyalty, should be aware that they are committing an offence and could be prosecuted.
“It’s vitally important that we speak to Bulle.
"My message to him, is to do the right thing and let us know where you are."
Medics tried to resuscitate the victim after the machete attack but the victim was pronounced dead at the scene in Chervil Rise, a part of Heath Town regularly troubled by violence near Wednesfield Road.
The area was cordoned off and forensic teams were at the scene late into the evening as the murder investigation began.
Police were also scene at another nearby address on Tuesday, while a post-mortem is due to be carried out on Wednesday.
A West Midlands Ambulance Service spokesman said: “We were called at 5:21pm on Monday to reports of a stabbing in Chervil Rise in Wolverhampton. The Midlands Air Ambulance from Cosford, two land ambulances, a paramedic officer and the Midlands Air Ambulance Critical Care car attended the scene.
"On arrival, crews found one patient, a man, in a critical condition. Sadly, despite best efforts, nothing could be done to save the man and he was confirmed dead at the scene.”
Anyone who sees Bulle is asked not to approach him but contact police immediately.