Clinton is expected to meet with Israeli Prime Minister Benjamin Netanyahu on Wednesday and hold additional talks with Palestinian Authority officials and Egyptian President Mohamed Morsi on Friday.
With the conflict in Gaza in its seventh day, the administration is pushing to end the violence, in hopes of averting a ground invasion of Gaza by Israeli forces.
The White House has leaned on Morsi, in particular, to rein in terrorist attacks from the Hamas-controlled territory, with President Obama calling the Egyptian president again Tuesday evening to discuss the situation.
Morsi predicted Tuesday that the violence would soon cease.
“The efforts to conclude a truce between the Palestinian and Israeli sides will produce positive results in the next few hours,” Morsi said, according to Egypt's MENA news agency.
The reports of an imminent ceasefire also comes as the U.S. mission to the United Nations on Tuesday reportedly blocked a Morocco-sponsored Security Council statement calling on Israel and Hamas to “immediately halt all violence” in Gaza.
Reports suggest U.S. officials did not believe the statement placed sufficient criticism on Hamas for the recent spate of rocket attacks that sparked Israeli retaliation. Russia has vowed to push a vote on its own resolution calling for an end to the violence if the Moroccan statement failed.
“We think it’s vitally important that this council, by its action, or non-action, is reinforcing the prospects for an agreed cessation” of hostilities, U.S. Ambassador Susan Rice said Monday. “That’s got to be agreed between the parties to be meaningful or sustainable. That is our principal objective in these discussions.”
Israel last week began an air offensive last week hitting Hamas officials and targets in Gaza in response to the rise in rocket attacks from the territory. Israeli officials have not ruled out a ground offensive in Gaza.
While the U.S. has been publicly supportive of the operation, Obama has also said he hopes Israel's objectives can be achieved without "ramping up" military efforts in Gaza.
On Tuesday, the White House dispatched Clinton to the region in hopes of hammering out an agreement to bring the violence to an end.
—This story was last updated at 11:58 a.m.