Police questioning Constance Marten and Mark Gordon believe the baby, whose remains were found in Brighton, may have been dead for “several weeks” and have been unable to confirm its gender.
The Metropolitan Police said it was “too early” to provide a specific date as to when the baby died, adding that a post-mortem examination has not yet taken place.
In a statement, Detective Superintendent Lewis Basford said: “Despite this, based on our inquiries we’ve carried out so far, we believe sadly the baby may have been dead for several weeks before they were found.
“It is too early for us to provide a more specific date.”
He added that Marten and Gordon remain in custody and the case has been referred to the police watchdog.
The body was found in a wooded area of Brighton close to where Marten, 35, and Gordon, 48, were arrested on Monday.
Detective Superintendent Basford said officers investigating the case are “devastated” by its outcome.
Confirming the discovery of the baby’s remains on Wednesday night, he said: “This is an outcome that myself and that many officers who have been part of this search had hoped would not happen.”
He added: “A crime scene is in place and work at the location is expected to continue for some time.”
Marten and Gordon had been missing with the baby since 5 January when their car caught fire on the M61 near Bolton.
The pair remain in custody after police were granted a 36-hour custody extension by city magistrates on Wednesday.
It is believed Marten, who comes from an aristocratic family with royal connections, gave birth to her baby one or two days before the incident, and neither she nor the child received any medical attention while the family were missing.
Police lodged an appeal for the couple to come forward, saying the baby was “at the heart of the investigation” and that concerns were rising “day by day” for the child’s wellbeing.
Marten and Gordon were spotted numerous times around the UK, including in Liverpool, Essex, south London and East Sussex, before their arrest in Brighton.
The pair were found without the child and were detained on suspicion of child neglect, and were later further arrested over alleged gross negligence manslaughter.
While in custody, they refused to divulge information on the location or welfare of the baby, and detectives were given another 36 hours to question the couple.