The 19-year-old who joined the radical Islamic group in 2015 is pregnant and lives in a Syrian refugee camp. After the death of two children, she wants to return to London.
The family's lawyer said earlier on Friday there were strong but as yet unconfirmed reports that Begum's son had died.
"The tragic death of Shamima Begum's baby, Jarrah, is a stain on the conscience of this government," Diane Abbott, the opposition home affairs spokeswoman said.