25-year-old Timothy Robinson was stabbed in the face and chest after parking his car in a Battersea street in London on Sunday evening.
At a news conference Detective Superintendent Trevor Shepherd said he wanted to speak to a 13-year-old boy who was seen sitting on a mountain bike near the spot where the attack took place.
"This young lad has actually seen the fight in the street, it really is vital that we speak to him," said Detective Superintendent Shepherd.
Devastated family
Mr Robinson was attacked after picking up his girlfriend Jemma Joyce, 26, from London's West End and driving her back to Warriner Gardens in his Audi.
He died in the intensive care department at St Thomas' Hospital in central London on Wednesday afternoon.
His family said they have been "devastated" by his death.
In a statement read by police on Thursday, the family said: "Tim was a wonderful person, much loved by his family, his partner Jemma and her family and all his many friends.
"We are devastated by his death."
The family paid tribute to the "exemplary care" given to Mr Robinson at St Thomas's Hospital in central London where he was treated.
The statement added: "The messages of sympathy and support we have received from so many people are deeply appreciated."
Girlfriend's screams
Det Supt Shepherd said there appeared to be no motive for the attack and Ms Joyce had been left "traumatised".
Ms Joyce, a student teacher, was approached by two men as Mr Robinson, a partner in an estate agency in South Kensington, west London, parked his Audi car.
As he returned to his girlfriend's side an altercation took place and the two men stabbed him repeatedly in the face, chest and upper arm.
Neighbours and passers-by were alerted by the screams of Ms Joyce.
Det Supt Shepherd said the two men had engaged the estate agent's girlfriend in conversation by asking her a question as Mr Robinson parked the car.
As the estate agent returned to the pavement, beside Ms Joyce, the two men started a fight.
"At present we are unsure of the motive," said Detective Superintendent Shepherd.
Brief conversation
"Possibilities have been suggested and are being followed, there is no evidence of any particular motive at the moment.
"It seems that the two suspects asked Tim's girlfriend a question, engaged her in conversation for a few moments.
"He finished parking the car and returned to the pavement and then started a conversation with the suspects who then started to attack him."
The officer said a motorist in a black Fiat Punto had chased one of the suspects in a car for about 50 yards, sounding the horn of the vehicle.
Mr Shepherd said the two men were black, aged in the early 20s, about 5ft 10ins in height, both had short hair and were wearing casual clothing.
The News of the World today have offered a £10,000 reward for any information leading to the capture of Mr Robinson's killers.