"Family are very disappointed with the Home Office's intention to have an order made depriving Shamima of her citizenship," their lawyer Tasnime Akunjee said on Twitter.
"We are considering all legal avenues to challenge this decision," he wrote.
ITV News reported that the Home Office has sent a letter to Begum's mother, received Tuesday, notifying the family of the decision, which it said Begum had the right to appeal.
The Home Office -- Britain's interior ministry -- did not immediately reply to a request for comment from AFP.
The 19-year-old East London native joined IS in Syria in 2015 along with two classmates.
She is currently in a refugee camp in northeast Syria where she fled fighting in the east of the country along with hundreds of other people with links to IS.
At the weekend she gave birth to her third child, and asked the British authorities to show "compassion" by allowing her to raise the baby in Britain -- while expressing no regret over having joined IS.
Her other two babies died, apparently from illness and malnutrition.
Begum's case points up a dilemma facing many European countries, divided over whether to bar jihadists from returning home over security concerns, or allowing them to return to face prosecution.
Shamima is allowed to appeal the decision and her family lawyer said they are 'considering all legal avenues to challenge this decision'.