The sources have told Sky News the writer had been “cut up” and his face “disfigured”.
One source also suggested Mr Khashoggi’s remains were discovered in the garden of the Saudi consul general’s home – situated around 500 metres away from the consulate.
It contradicts the explanation being made by Saudi officials that the body was rolled up in a carpet and handed to a local collaborator who was tasked with disposing of the evidence.
Theresa May’s spokesman said reports of Mr Khashoggi’s body parts being found were “deeply disturbing”.
“The location of Mr Khashoggi’s body is just one of the questions we need answers to and as such we await the full results of the Turkish investigation,” he said.
It comes as pictures have been published of the journalist’s son, Salah Khashoggi, meeting the Gulf kingdom’s ruler, King Salman, and his son crown prince Mohamed Bin Salman, at the Yamama Palace in Riyadh on Tuesday.
Mr Khashoggi’s brother, Sahel, was also at the meeting at which the king and crown prince expressed their condolences over the Washington Post columnist’s death.
A family friend told the AP news agency Salah Khashoggi had been under a travel ban and barred from leaving the kingdom since last year as a result of his father’s criticism of the regime.
Saudi authorities have not confirmed the restrictions.
Turkey’s president earlier said Mr Khashoggi’s body had not been found and demanded Saudi officials reveal its whereabouts.
Recep Tayyip Erdogan, who had promised the “naked truth” about the killing, said: “Why has the body of someone who was officially said to be killed not been found yet?”
The Turkish president called on Saudi Arabia to hold those responsible to account in a dramatic speech to parliament.
He described the journalist’s killing as “murder” – the first time this accusation has been made by a named Turkish politician – adding the killing was premeditated and planned days before.
There was also no mention of an alleged audio recording that Turkish authorities claim to have of Mr Khashoggi’s death that supposedly confirms he was tortured, killed, had his fingers cut off and was dismembered.
Turkish political analysts believe the Saudis would prefer to perpetuate reports that the body was not disfigured or cut up to avoid more uncomfortable questions and explanations about how the body came to be defiled.
The apparent discovery of Mr Khashoggi’s body parts – and Mr Erdogan’s version of events based on what he described as “new evidence and information” – both contradict Saudi Arabia’s explanation for his death.
It has said Mr Khashoggi died in a “fist fight” at the Saudi consulate in Istanbul on 2 October.
Mr Khashoggi was a known critic of the Saudi government and crown prince Mohammed bin Salman.
The Turkish president did not mention the crown prince in his speech, though officials linked to the royal have been implicated in the killing.
Saudi Arabia has said the heir-apparent of the world’s top oil exporter was not involved, but any major decision must be signed off by the highest powers within its ruling Al Saud family.
Mr Erdogan said Riyadh’s suggestion it was a rogue operation “will not satisfy us” and said there should be no diplomatic immunity for his killers.
He said 18 people had been arrested – three from the consulate and a further 15 who are believed to be part of a hit squad who flew to Istanbul to carry out the killing – and they should all stand trial in Istanbul.
“To blame such an incident on a handful of security and intelligence members would not satisfy us or the international community,” Mr Erdogan said.
“Saudi Arabia has taken an important step by admitting the murder.
“As of now we expect of them to openly bring to light those responsible – from the highest ranked to the lowest – and to bring them to justice.”