The BBC’s security correspondent Frank Gardner said Jones had been a useful propaganda agent for IS on social media and her death would be “significant”.
Whitehall officials have declined to comment publicly. However, they have not denied the story, and US sources are confident she was killed in an unmanned drone strike in June, our correspondent added.
She was reportedly killed close to the border between Syria and Iraq by a US Air Force strike.
Jones, 48 – who had no previous military training – had been married to the jihadist Junaid Hussain, who was killed in 2015 in a drone strike.
Previously a punk musician, she had been used to recruit western girls to the group and posted threatening messages to Christians in the UK.
Jones, who was born in Greenwich, London, also encouraged individuals to carry out attacks in Britain, offering guidance on how to construct home-made bombs.
She used her Twitter account to provide practical advice on how to travel to Syria and shared pictures of herself posing with weapons.
She won’t be missed.