Speaking through family lawyer Tansime Akunjee, Begum's mother, Asma, was cited by the British news outlet The Sun as saying that she wants her grandson to be taken away from Begum and brought to the United Kingdom because she "doesn't want the grandchild indoctrinated".
Isis fighter Yago Riedijk, 27, is being held in a Kurdish-run detention centre in northern Syria.
Riedijk faces a six-year prison sentence for "joining a terror organisation" if he returns to the Netherlands.
As the ISIS fighter's put up a final fight against USA -backed Kurdish forces in Baghuz, there are hundreds of ISIS fighters like Riedijk who have surrendered and are in captivity.
He said he rejected ISIL and had tried to leave the group after he was tortured by its members who accused him of being a spy for the Netherlands. But he now admits that joining the ISIS was a "big mistake".
He said: 'I don't think I remember that, knowing that back home. "I've thrown away years of my life". "It was not my life". "I wish I had stayed low and found a different way to contact my family", she told The Sunday Telegraph in an interview on 24 February.
He added: "Technically I was part of (the group). It's something that's not acceptable".
She was stranded in the al-Hawl refugee camp as ISIS fighters are driven to destruction by coalition forces.
Although Yago Riedijk admitted to fighting for IS, he told the broadcaster he is keen to return home to the Netherlands with Begum and their baby son. I now understand the privileges I lived with.
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A spokesperson for the Dutch Immigration and Naturalisation Service (IND) said it can not comment on individual cases, but added that to live in the Netherlands with a Dutch national a spouse or partner would need a resident permit - which would require a valid passport or other travel document.
However, when he was challenged about the many violent acts committed by the group against the Syrian people and those of other nationalities, he said: "Either I was not aware of that or it happened after I came (to Syria)".
Riedijk and Begum got married in 2015, days after she arrived in territory controlled by the Islamic State in Syria. Riedijk was 23 years-old then.
"Shamima is highly damaged and the family don't want the newborn brought up by her in that state of mind", he said.
Describing how he met the schoolgirl from east London in the women's centre in Raqqa, he said he was initially not interested because she was too young.
"Hopefully soon we'll be together again and things will turn out alright, hopefully". "He had a slave". When asked by a Sky News reporter, "Did you know what Islamic State [ISIS] were doing when you left for Syria?"
"Luckily, I did not have direct involvement in.hurting or harming people". Bangladesh, her mother's nationality, has also denied her citizenship, saying that she will not be allowed into the country.
"Why should the Netherlands have to take responsibility for this?"