The grim discovery was made in the Parioli neighbourhood in the north of the capital, by a young woman believed to have been searching through the bins.
Repubblica have identified the victim as 59-year-old Nicoletta Diotallevi. According to the same report, the victim lived with her 62-year old brother Maurizio, who is being questioned by police.
According to Il Messaggero, the victim's brother has confessed to the murder. The same daily reports that the man was seen leaving his home, which he shared with the victim, at around 1.30am yesterday.
According to a police spokesperson cited in Repubblica, the legs had likely been sawn off and dumped in the refuse container the previous night, "judging from the initial state of decomposition".
Forensic experts were combing through surveillance footage from the neighbourhood on Wednesday and found various other body parts belonging to the victim near where the legs were found.
The victim's body parts were allegedly to bits with an ax at her home before being dumped in the rubbish container, according to the same report in Il Messaggero.
A man was seen walking away from the bin on Monday night, when the legs were dumped according to forensic analysis, and his number plate has been partly identified, Repubblica reported.
It remains unclear if the numberplate is the same as that on the car of the victim's brother.
Several reports in Italian dailies claim money issues between the siblings could have been the motive behind the grotesque sororicide.
In 2015, Rome was shaken when a severed leg tattooed with the words "Today is a good day to die" was fished out of a tributary of the River Tiber, which flows through Rome, according to AFP.
That leg, which had been severed above the knee, belonged to a hardcore fan of the Rome football club Lazio who was a known drug user and had a criminal record.
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