The man has been in the hospital in critical condition since the fire on August 21st last year on Westbury Road off Cooper Lane, in the city's BD6 area.
Ms. Gawys, 29, died at the scene of Westbury Road off Cooper Lane, in the city's BD6 area, and her three children – Dennisty, nine. Oscar, 5; Aubrey, 22 months old, died from a hospital injury.
Mohammed Shabie, 44, of Alice Street, Kaylee, and Calm Sunderland, 25, of Calton Street, Kaylee, pleaded not guilty to the murder of Ms. Gawys and her child at Bradford Crown Court.
Both men also pleaded not guilty to the attempted murder of Antonia Gawys.
They are scheduled to go to trial from March 4th this year.
The pair appeared at Bradford Crown Court over a video link from HMP Hull on Tuesday.
The hearing was arrested on suspicion of murder and told that another man in the hospital had regained consciousness.
The incident has been postponed to another hearing and is scheduled to take place on February 24th.