Jones, a former punk rocker, travelled to Syria from her home in Kent in 2013, taking her then 11-year-old son with her, to marry an ISIS terrorist she had met online. Spokesman Maj Adrian Rankine-Galloway said, "I do not have any information that would substantiate that report but that could change and we are looking into this".
It is noted that her 12-year-old son died with his mother.
Once in Syria, she married ISIS member Junaid Hussain, with whom she was having an online relationship.More news: Iran has 'all options on table' if U.S. blacklists Revolutionary Guards
Asked about reports Jones' son was killed in the strike, Maj Gen Chapman added: "It is a hard one because under the UN Charters he is under the age of what we would classify as a soldier". She was nicknamed the "White Widow" after this. She was marked as a "high priority" on the US's kill list earlier this year, the newspaper added.
If reports of Jones' death are true, she would be the sixth Briton killed by drones in Syria. She also encouraged them to carry out attacks in Britain and offered lessons on making home-made bombs.
Jones, 50, also went by the name Sakinah Hussain, or Umm Hussain al-Britani, and once said she wanted to behead Christians with a "blunt knife".
Officials said conditions on the ground prevent them from knowing for certain if Jones is dead, but her social media activity has been silent for months.
Major General Chip Chapman, the former MoD head of counter terror, told Sky News Jones was a "significant" target for the United States and UK.