Anxiang Du, 52, is being sought in connection with the deaths of Manchester Metropolitan University lecturer Jifeng Ding and his family.
Mr Ding, his wife Helen Chui, and daughters Alice and Xing, were found stabbed in their home in Pioneer Close, Wootton, Northampton, on Sunday night.
Police said Mr Du, from Coventry, had left a suicide note.
Mr Du left a note to his family implying it was time to say goodbye.
He is understood to have been a business associate of Ms Chui dealing in herbal remedies.
Mr Du left his home in Coventry at 1030 BST on Friday to go to work in Birmingham but never returned.
He was last seen on 29 April in Birmingham City Centre, Pallasades Shopping Centre and was wearing a white baseball cap, brown waist-length coat, grey trousers, a blue woollen top and black leather shoes.
He was described by police as being of slim build with a bald patch.
Police said they were still looking for a murder weapon.Jifeng Ding and Alice Ding died from stab wounds, police have revealed
Officers said the family, who are of Chinese descent, had suffered knife wounds.
Det Supt Glyn Timmins said: "The public should be cautious. The reason being is that, obviously having left a suicide note Mr Du had a particular state of mind.
"What I can say is that he's likely to be frightened, he's likely to be quite desperate and certainly when, and if, he sees this in the media he's certainly going to be very anxious and nervous.
"Therefore I think the prudent thing to do would be to assume that Mr Du should not be approached and that's a job for the police if and when he's sighted."
Police also want to trace a silver five-door Vauxhall Corsa, registration BG60 PMO, that was hired by one of the family members and was last seen on Friday.
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