At about 5pm on Friday 12 June, a man and a woman called at an address in Cottingley Drive and engaged in an argument with the male occupant.
The man then produced a knife and attacked the 35-year-old male, causing serious cuts to his right arm.
He was taken to hospital for treatment and was later released.
Armed officers were deployed to the area, but were unable to locate the suspects.
The man is described as black, in his mid-twenties and was wearing a blue ‘Adidas’ tracksuit.
The woman is described as white, around similar age and was said to have reddish brown hair.
She was believed to be wearing a black top and black leggings.
Acting Detective Inspector Claudine Binns, of Leeds District CID, said:
“We are following up a number of leads in relation to this incident, but we would like to hear from anyone who witnessed anything suspicious in the area around the above time to come forward.”
Anyone with information is asked to contact DC 2043 Houghton at Leeds District CID on 101 or Crimestoppers anonymously on 0800 555111.