Biden's national security adviser Jake Sullivan said the US president would soon speak with Egyptian President Abdel Fattah al-Sisi about the negotiations.
Sullivan said it remained to be seen whether a deal would actually be reached.
An Israeli official said on Monday that negotiations were in advanced stages for the release of up to 33 hostages as part of a Gaza Strip ceasefire deal.
"We are not sure if it is hours or days or more," the official, speaking on condition of anonymity, said about the timing of a potential deal.
Hamas fighters entered Israel in October 2023, killing about 1200 people and taking 250 hostages. (AP PHOTO)
Another round of ceasefire talks will be held in Doha on Tuesday morning to finalise remaining details related to the deal, an official briefed on the negotiations told Reuters on Monday.
A deal to end the war between Israel and Hamas is "closer than it's ever been," the official said, adding that Trump's Middle East envoy Steve Witkoff, outgoing Biden administration envoy Brett McGurk and Israel's Mossad chief David Barnea and Shin Bet head Ronen Bar were expected to attend.
Mediators gave Israel and Hamas a final draft of a deal on Monday, an official briefed on the negotiations said, after a midnight "breakthrough".
The official said the text for a ceasefire and release of hostages was presented by Qatar to both sides at talks in Doha, which included the chiefs of Israel's Mossad and Shin Bet spy agencies and Qatar's prime minister.
Israel launched its assault in the Gaza Strip after Hamas fighters stormed across its borders in October 2023, killing 1200 people and taking more than 250 hostages, according to Israeli tallies.
Since then, more than 46,000 people have been killed in the strip, according to Palestinian health officials, with much of the enclave laid to waste and most of its population displaced.