His stance is likely to be significant, as it is the group's military wing that has direct control over whether the hostages are released.
Key objections are understood to include the demand for full disarmament, as well as the proposal for an "International Stabilisation Force" in Gaza, which the group is reported to see as "a new form of occupation".
The BBC piece seemingly contradicts a CBS report from Tuesday, which suggested that Hamas was likely to accept the deal and could deliver its response as soon as today.
President Trump subsequently said he would give Hamas "three or four days" to reply, but that he "has a feeling" it will say yes.
Trump has also said that, if the deal is rejected, Israel would have Washington's "full backing" to "finish the job" in Gaza.
It comes after the deal was embraced by hostage families, with the Hostages and Missing Families Forum saying: “After almost two years of unimaginable anguish, we stand at a historic turning point.
"This is a historic agreement that will allow our people to heal, end the war, and chart a new future for the Middle East.”
