Begum, who fled London to join the terror group in 2015, has been trying to return to the United Kingdom but was recently stripped of her citizenship.
The baby died later that day.
Home Secretary Said Avid said he did not know if the baby, a British citizen, had died.
As the Begum family lawyer emphasised the reports were unconfirmed, others said people in the camp had reported that the baby was still alive.
A spokesman for the Home Office told CNN that the Home Secretary can deprive someone of their British citizenship "where it would not render the individual stateless".
She married a Dutch man within days of her arrival in Syria when she was 15.
"I don't really want to stay here, I don't want to take care of my child in this camp because I'm afraid he might even die in this camp", she said in an interview with United Kingdom broadcaster Sky News shortly after giving birth.
The British Government could not confirm the reports.
Shamima Begum captured on CCTV in 2015 on her way to the Middle East. Credit PA
Speaking from al-Hawl before giving birth, Begum told United Kingdom newspaper The Times that she wanted to come home to have her child.
Miss Begum entered the Al-Hol camp for displaced Daesh families in Syria's north after fleeing the brutal fighting that was taking place in the group's last stronghold of Baghuz, on the east bank of the Euphrates river. Now 19, she has already lost two children prior to her latest child being born.