What is happening with talks between Israel, the US and Hamas?

An Israeli negotiating team has reportedly extended its stay in the Qatari capital Doha, a day after the US envoy to the Middle East Steve Witkoff was in town to try and find a path forward between Israel and Hamas.

The deal reportedly on the cards is an extension of the ceasefire for up to 60 days in exchange for between five and 10 living Israeli captives held in Gaza.While Hamas has previously rejected a similar deal, they may be more amenable after direct meetings between US hostage envoy Adam Boehler and top Hamas officials in recent weeks. Boehler had said that the meetings went well and suggested a deal was on the cards for a potential long-term ceasefire, prompting a backlash from Israel and pro-Israeli US politicians.

There are even reports that Boehler has been taken off the Israel-Gaza file, but those reports may be premature.What is the deal currently being negotiated?
A deal between Israel and Hamas had already been reached, which included three phases and was eventually to lead to a permanent ceasefire. The first phase involved a limited swap of Israeli captives and Palestinian prisoners, as well as a temporary ceasefire and Israel allowing an increased amount of humanitarian aid into Gaza. The details of the second phase were still to be negotiated, but the previous US administration of President Joe Biden made it clear that the first phase would continue until the second phase could be agreed upon.