According to The Sun newspaper, a US Air Force Predator drone was used to kill Jones, who had adopted the Islamic nom de guerre of Umm Hussain al-Britani.
Jones, who was nicknamed the "White Widow", is believed to have publicized a list of American military personnel to be targeted by ISIS militants, led a group of female terrorists, and acted as a top recruiter online.
Her young son Jojo was not known to be with her at the time of the strike and was not intentionally targeted, though he is presumed dead, as well.
The Pentagon said it's looking into reports that a British Islamic State supporter known as the "White Widow" was killed by an airstrike this summer. Later, she became interested in music and played bass guitar in an all-girl punk band called Krunch.
Jones, 50, took her son Jojo and left her home in Chatham, Kent, for Syria to join her husband Junaid Hussain in 2013.
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Mr Fallon also stressed that IS was preparing and inspiring terror attacks in the UK.
Jones has used her son-who has previously appeared in an ISIS execution video-as a human shield in the past, prompting speculation that he may have been killed in the drone strike.
"The premise that Sally Jones and her son are dead is probably accurate", a United Kingdom government source was quoted as saying by The Times.
Mr Corbyn, said it was hard to answer a question about whether he would have ordered a drone strike to kill Jones if British troops had been at risk, as it was hypothetical.
Former Ministry of Defence head of counter terror Major General Chip Chapman said Jones' alliance with Hussain and her recruitment role would have made her a "significant" target.