Jones was killed close to the border between Syria and Iraq by a US Air Force strike in June, according to The Sun.
She and her husband Junaid Hussain went to Syria in 2013 to join IS.
He was killed by a US drone in 2015, and had allegedly been planning "barbaric attacks against the West", including terror plots targeting "high profile public commemorations" this summer.
News of her death was not made public amid fears that her 12-year-old son Jojo may also have been killed, according to The Sun.
Jones, who was previously a member of an all-girl punk rock group, left her home in Chatham, Kent, after converting to Islam.
She used her Twitter account to recruit women and provided practical advice on how to travel to Syria.
Born in Greenwich, London, she encouraged individuals to carry out attacks in Britain, offering guidance on how to construct home-made bombs.
She has also shared pictures of herself posing with weapons.
Jones also posted messages in support of IS as well as extremist comments such as: "You Christians all need beheading with a nice blunt knife and stuck on the railings at Raqqa ... Come here I'll do it for you."
A Foreign Office spokeswoman said: "We do not comment on matters of national security."
Major General Chip Chapman, the former MoD head of counter terror, said Jones would have been a "significant" target as a result of her alliance with Hussain and her role in recruiting IS fighters.
Referring to reports her son was killed in the strike, he added: "It is a difficult one because under the UN Charters he is under the age of what we would classify as a soldier."
He continued: "Even if he got up to really bad things, he shouldn't have been targeted.
"We don't know for sure whether he was with her or not."