The prominent lawmakers were among a bipartisan group of U.S. senators who earlier met in Tel Aviv with Israeli Prime Minister Benjamin Netanyahu, who on Sunday repeated his backing for Trump's controversial vision for Gaza.
Israeli officials have latched onto Trump's proposal, with Israeli Defense Minister Israel Katz instructing the military to prepare a plan that would allow for Palestinians in Gaza to leave voluntarily.
But Graham, a longtime ally of Trump and a key Republican in Congress with influence on foreign policy and national security matters, told reporters there was little appetite in the Senate "for America to take over Gaza in any way, shape or form."
Blumenthal simply said the plan was a "non-starter."
Trump's proposal has been widely denounced by Arab officials, while some critics have said it equates to ethnic cleansing. Netanyahu as recently as Monday said that the Palestinians in Gaza should be given the choice to leave.
Katz said on Monday that he would establish a directorate within the ministry for the voluntary departure of Palestinians from Gaza.
"The one thing that President Trump has done, he started a discussion that was long overdue," Graham said, saying that Arab states had "woken up" to finding a better alternative for Gaza.
Saudi, Emirati, Jordanian and Egyptian officials are expected to meet as soon as this month to discuss the future of Gaza, hoping to devise a plan to counter Trump's proposal that has rattled nearly all Arab capitals after 16 months of war in Gaza.
Blumenthal said Jordan's King Abdullah had convinced him that Arab states would present a plan that covers normalising ties with Israel, self-determination for the Palestinians, regional defense arrangements and security for Israel.
"If those components are part of a realistic plan, it could be a game changer for the region," he said.
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