The two men remain in police custody more than 24 hours after being arrested.
A 56-year-old from Bilston and a 76-year-old from Kingstanding in Birmingham were arrested on Thursday night and are still being questioned by detectives over Jomaa Jerrare's death.
Staffordshire Police confirmed that detectives had been granted additional time to question the two suspects.
Detectives investigating the death of Jomaa Jerrare in Perton have been given further time to continue questioning two men. A 76-year-old man from Birmingham, and a 56-year-old man from Bilston were arrested o/night on Thurs (August 12/13) on suspicion of murder. pic.twitter.com/zvButpRUxV— Staffordshire Police (@StaffsPolice) August 14, 2021
Ms Jerrare, aged 52 and from Heath Town in Wolverhampton, was found dead in a layby on Bridgnorth Road in Perton in the early hours of Monday morning.
The suspects were the second and third people to be arrested over her death, with the first man released after accounting for why he was in the area near where Ms Jerrare was found.
It took police two days to identify Ms Jerrare, with officers initially believing the body belonged to a younger woman.
Interactive map shows key locations:
The severity of the burns to her body meant it was difficult to establish her age, gender and ethnicity.
It comes after the officer leading the investigation appealed for information regarding Ms Jerrare's recent movements from the layby where she was found.
Prior to her death Ms Jerrare had not been seen by her family for six weeks or by neighbours for four weeks.
But Detective Superintendent Tom Chisholm said because of her chaotic lifestyle, which had involved substance abuse, it was not unusual for her to be out of contact for a length of time. She had not been reported missing.
He said she had "lots of friends and acquaintances" and teams were trying to establish if she had any "long-term partners".
Ms Jerrare lived alone in Heath Town and had lived in and around Wolverhampton for most of her life.
Police believe that Ms Jerrare was killed before being driven to the layby but it is not yet known where or how she died after a post mortem failed to confirm the cause of death.
Meanwhile officers also searched the high-rise building on Woden Road in Heath Town where Ms Jerrare lived.