Twenty firefighters tackled the blaze, which started shortly after midnight yesterday in the middle England city.
"At this stage we are not able to confirm where in the house the fire broke out or if anyone else was injured," a South Yorkshire Police spokesperson said.
A police cordon still remain in place on the street as the investigation into the case continues.
A relative, Ishfaq Kayani, spoke to the BBC about the "tragedy beyond imagination".
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The 54-year-old aunt had initially escaped the fire but went back into the house in an attempt to rescue them.
"She gave her life trying to save her grandchildren," Kayani said.
"The two boys who died were nine-year-old Adhyan Nazim and seven-year-old Amaan Nazim. Their mother escaped the fire and their father was at work at the time", he said
"The whole family is in a state of shock, devastated. The whole community is in a sombre mood. Friends, relatives, we're all in huge, huge shock. Just in a matter of minutes the whole family has been destroyed. The whole family has gone", he said.