Zane died during floods in Surrey in 2014. An inquest in 2016 found carbon monoxide emitted by a petrol pump, which the boy's parents hired to clear flood water, poisoned him in his sleep.
But his parents contested the inquest verdict, and have argued the flood water was contaminated with toxic hydrogen cyanide from a nearby lake, located on a former landfill site, and claimed that was the ultimate cause for their son's death.
More than 30 MPs have signed an early day motion calling for an "independent panel inquiry with full powers to compel disclosure into the death".
Mr Burgon told the Commons that the boy's parents were watching proceedings from the public gallery. The MP said: "Zane was just seven when he died following floods 10 years ago this month. The fire brigade detected hydrogen cyanide multiple times."
The MP said Zane's parents have been "fighting for the truth about their son's death ever since". He said: "A duty of candour would have helped them to get it."
"But, in lieu of that, will the Government establish an independent panel inquiry with full disclosure so that all the evidence can be reviewed by experts, and so we can finally get the truth about what happened to an innocent seven-year-old boy and so that justice can be done?"
Mr Chalk said: "He raises a critically important case. Can I suggest that he and I speak to discuss it and see what further steps can properly be taken in this difficult case."
Labour shadow justice minister Kevin Brennan welcomed the commitment to discuss the case, but said the Government had not gone far enough on requiring public authorities to act "with candour and transparency" and accused the Government of "persisting with a piecemeal approach".
Mr Chalk defended the Government's record, including adopting the Hillsborough Charter, which he said requires public bodies to approach public scrutiny with candour. But he said: "Of course, we will keep this under review."
Mr Chalk had earlier told the Commons that the Government has imposed a duty of candour on the police, and is legislating to create a "strong, permanent, and independent public advocate to speak up for victims and their families".