Searches have been carried out at properties in the West Midlands after human remains were found in two suitcases in the Forest of Dean.
Gloucestershire Police said DNA tests were being carried out to identify the female victim, and the cause of death was not yet known.
Officers made the discovery near Coleford on Tuesday evening.
A woman in her 20s and a man his 30s were arrested are continuing to be questioned, police said.
On Thursday afternoon detectives were given an additional 36 hours to continue questioning the man from Wolverhampton and the woman from Birmingham.
West Midlands Police said: “We’ve carried out searches at properties in Wolverhampton and Birmingham as part of the investigation.”
Meanwhile, a spokesperson for the Gloucestershire force said: “A post-mortem examination yesterday was found to be inconclusive and further examinations are ongoing to establish the cause of death.”
The remains were found when police responded to a call about a driver acting suspiciously just after 22:30 BST on Tuesday.
Searches have continued around the area of Stowfield Quarry, near Coleford, and some road closures remain in place.