Mick Philpott, 55, and his wife Mairead, 31, were arrested on Tuesday and were being held on suspicion of murder.
This morning, it was reported on BBC Radio Five Live that police had been granted a further 12 hours to continue their inquiries.
Jade Philpott, 10, and brothers John, nine, Jack, eight, Jessie, six and Jayden, five, died in the house fire on Victory Road on 11 May.
Their older brother, Duwayne, 13, died three days later in hospital.
All six children were asleep upstairs when the fire began in the early hours. Derbyshire Police said petrol was used to start the fire which was believed to have begun below the house's letterbox.
Father-of-17 Mick made headlines in 2006 after asking for a larger council house for his family Five days after the attack the couple held a brief press conference and thanked those who tried to rescue the children and members of the local community for their support.
According to the Telegraph, the arrests had been planned for several days. The newspaper's sources said that Mr Philpott's behaviour in recent days had been monitored.
One said: "He's been watched very closely from the outset."
Last week detectives removed the couple's caravan and minibus from outside the house for forensic examination.
Speaking after Tuesday's arrests, Assistant Chief Constable Steve Cotterill said: "In view of the arrests, I would urge anyone who may have been holding back, not felt comfortable to voice their concerns or not had the confidence, to do so now.
"The latest arrests are just one step further in the investigation. It is absolutely vital that if you know anything you think could help us, come forward now, do not wait any longer.
"What we need to do now is carefully take our time, question the two individuals concerned and piece it together with everything else we know to date."
UPDATE 30 MAY: Mick and Maired Philpott have been charged with the murder of their six children.
Speaking after the pair were charged, Assistant Chief Constable Steve Cotterill stressed that the police investigation was ongoing and urged anyone with information about the blaze to contact police.
He said: "Following the appeal yesterday a number of people have come forward with more information but I want to stress that the two charges this evening should not be seen as the end of the investigation.
"We are determined to get to the truth of what happened and still want people to speak to us to tell us what they know about this tragedy."
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