That's according to Reuters sources, coming as Israel pressed ahead with its biggest assault in a month in southern Gaza.
Qatar, the U.S. and Egypt have been mediating between the two sides for weeks over the release of Israeli captives, in return for a break in fighting, the release of Palestinian prisoners and more aid to the enclave.
But the plan is being held up, the sources said, with Hamas and Israel at odds over how to permanently end the Gaza war.
U.S., Qatari and Egyptian authorities did not immediately respond to requests for comment on the Reuters report.
Though on Tuesday, the White House did confirm that Middle East envoy Brett McGurk was in Cairo, for "active" talks over hostage release and aid, while declining to comment on reports of any ceasefire deal.
"Certainly, one of the things he's in the region talking about is the potential for another hostage deal, which would require a humanitarian pause of some length, to, to get that done."
Two Egyptian security sources said there was work underway to convince Hamas to accept a one-month truce to be followed by a permanent ceasefire.
However, Hamas is requesting guarantees that the permanent ceasefire would be carried out, to agree to the initial truce.
An Israeli government spokesperson said Tuesday, the country's goals of destroying Hamas' "governing and military capabilities" remained the same.
"There will be no ceasefire that leaves the hostages in Gaza and Hamas in power. Beyond that, we have nothing to elaborate."
Still, Israeli Prime Minister Benjamin Netanyahu is under increasing pressure to reach a ceasefire deal from his war cabinet and families of hostages.
Despite the difficulty of bridging the gap in the positions of the two sides, a source briefed on the discussions told Reuters, a deal could be agreed to "at any minute."
