A woman in her 20s was arrested on suspicion of murder, The Daily Telegraph reported.
The five children who died ranged in age from 5 to 10.
Derbyshire Police Assistant Chief Constable Steve Cotterill announced the arrest at a news conference, Sky News reported, without providing details on why she is a suspect.
"At the moment we are keeping a very, very open mind as to the cause of the fire," Cotterill said.
The children apparently were asleep upstairs and the parents were downstairs, Cotterill said.
Two adults and six children were taken to the Royal Derby Hospital, and one of the children was transferred to a hospital in Birmingham for specialized treatment.
The father was identified as Mick Philpott, who has 11 children.
Cotterill said Philpott had made a "valiant attempt" to save the children.
Sky News said Philpott had made national headlines several years ago over his attempts to obtain larger public housing for his family.