Shamima Begum, who had left London as a 15-year-old in 2015 to join the Islamic State group, had pleaded with British authorities before her baby was born to let her return to Britain to raise the child.
Shamima Begum, whose baby died in a Syrian camp last week, causing a controversy in Britain where Ms Begum has been stripped of her residency.
Home Secretary Sajid Javid previously said that the revocation of Ms Begum's citizenship would not apply to her son, saying: "Children should not suffer, so if a parent does lose their British citizenship it does not affect the rights of their child".
"The Government will continue to do whatever we can to prevent people from being drawn into terrorism and travelling to risky conflict zones".
Begum's infant son died Friday.
Her case has highlighted a dilemma facing many European countries, divided over whether to allow jihadists and IS sympathisers home to face prosecution or bar them from entry.
In a statement when reports of the baby's death were still unconfirmed, Mr Javid said: "Sadly there are probably many children, obviously perfectly innocent, who have been born in this war zone".
Two more jihadi brides who joined Islamic State of Iraq and the Levant are believed to have been stripped of their United Kingdom citizenship while living in a refugee camp in Syria.
Mr Hunt said he is working with International Development Secretary Penny Mordaunt on how children can be safely returned'.
Some politicians, like former Justice Minister Phillip Lee, have called for jihadi brides and their children to be allowed back into the UK. However, the Bangladesh foreign ministry said in a statement that Begum is not a Bangladeshi citizen, nor has she ever visited the country. "The UK and other countries of origin must take responsibility for their citizens inside north-east Syria", she added.
According to the BBC, the paramedic said the baby had been suffering from breathing difficulties and was taken to a doctor on Thursday morning.
Begum said that during her time with ISIS she was "just a housewife" and there was no evidence of her "doing anything risky".
A decision by Britain to strip a teenage girl of her citizenship after she joined Islamic State in Syria was described as a "stain on the conscience" of the government on Saturday after her three-week old baby died.