Toronto Police have named a man found at the scene of a downtown fire and homicide last week as a person of interest.

Det. Scott Whittemore of the service's homicide squad told CTV News on Tuesday that Fashar Badakhshad, 27, is currently their only person of interest.

Badakhshad was also injured in the July 2 fire at a 502 Huron St. rooming house. He remains in hospital in critical condition.

A 24-year-old woman at the scene was found to have died of stab wounds and burns to her body. Police said Monday the woman was a homicide victim, the city's 26th of 2010.

Whittemore said that Badakhshad and the victim knew each other, but police are still investigating the extent of their relationship.

Const. Isabel Cotton, a Toronto Police spokesperson, said the "person of interest" designation means that Badakhshad isn't formally considered a suspect at this time.

As the investigation proceeds, "we will be looking at what he was doing at the time of the homicide," she said.