Qatar has been seeking to play a relevant role in Israel’s Gaza policy amid the crisis with Hamas that has unfolded over the last six months. But those efforts have been frustrated as Qatar is isolated by Washington’s drive for a “deal of the century” and Doha’s own disputes with its Gulf neighbors. Recent cease-fire discussions, however, may now bring Qatar back into the group of countries that are working to avoid another conflict between Jerusalem and Gaza.Channel 10 reported last week that in June, Defense Minister Avigdor Liberman met in Cyprus with Qatar’s Gaza envoy, Mohammed Al-Emadi. At the top of Qatar’s list of concerns was the humanitarian issue, in which Qatar has taken a key interest for a decade. Doha could provide up to $350 million as part of a new deal to keep the peace between Israel and the Hamas-ruled Gaza Strip. Since 2014, it has already provided around $800 million.On Thursday, another report said that Prime Minister Benjamin Netanyahu met with Egyptian intelligence chief Maj.-Gen. Abbas Kamel. The complex discussions between Israel and Egypt, Hamas and Egypt, the US and Qatar, and – at least in the background – between Israel and Qatar, are the backdrop to the current attempt to create a long-term cease-fire with Hamas.In July, Al-Emadi told Al Jazeera that Qatar was discussing a fiveor 10-year cease-fire with Israel by passing messages to Hamas and the US.“The Egyptians are indeed involved,” he said. “However, the problem is the Egyptians are not trusted by Hamas. This is because more than a year ago, the Egyptians made many promises to Hamas to achieve reconciliation with Fatah, among other things, but they did not deliver on their promises.”So the deeper story is that Al-Emadi has sought to portray Qatar as the “credible” partner for “both sides.” Who are those sides, though? Hamas and Fatah? Hamas and Egypt? Hamas and Israel? Or maybe Hamas and the US? In June 2017, Israeli politicians and experts praised the decision by Saudi Arabia and its allies, including the United Arab Emirates and Egypt, to cut ties with Qatar. Riyadh blamed Qatar for supporting extremism in the region, pointing to Hamas, Hezbollah and to the hosting by Al Jazeera of extremists on its Arabic station. The immediate effect of this decision was that Qatar formed a closer bond with Turkey as Ankara sent troops to defend the emirate.Since the US announced in December 2017 that it would move its embassy in Israel to Jerusalem, the Palestinian Authority leadership has also grown closer to Turkey. PA President Mahmoud Abbas recently said that Ramallah stood with Ankara in the face of US pressure. Abbas also held talks in Jordan last week and rejected the US peace plan before he flew to Qatar. This creates a complicated mess, but with two blocs of discernible partners. Qatar, Turkey, the PA and Hamas have differing degrees of relations. Israel, Egypt and the US enjoy amicable relations. So the discussion for a cease-fire between Israel and Hamas takes place in the shadow of Qatar’s desire to play a role in both camps.What role is this? In his meetings in Doha in early August, Abbas reportedly praised the efforts of Qatar in rebuilding the Gaza Strip. But he pointed out that these efforts went “through the legitimate authority and the Palestinian government.”The Egyptian intelligence chief came to Israel last week but didn’t meet with Abbas, who was apparently angered that the deal appeared to give legitimacy to Hamas’s control of the Gaza Strip. So Abbas wants humanitarian aid to flow via Ramallah and does not want to empower Hamas as if it is its own authority.Qatar, when it discusses Gaza, doesn’t always mention the Palestinian Authority, though. “If we are helping Hamas, do you think the Israelis would allow us to go inside and come out?” Al-Emadi asked in February.Even more bizarre in the recent discussions are claims by Al Mayadeen TV that Hamas would get some kind of sea corridor to Cyprus, and that Qatar would pay salaries in Gaza, bypassing Ramallah and the PA’s sanctions on salaries in Gaza.It appears that Doha is willing to do whatever is necessary to play a role. This is in part because it has been trying to show its relevance to Washington. Last year, it sought to lobby influencers in DC through pro-Israel voices and paid lobbyists. That didn’t work. So Qatar reached out to Jared Kushner and Jason Greenblatt, who had been tapped by Trump to push for a peace deal.As recently as June 21, the day before the Qataris allegedly met Liberman in Cyprus, the emir met the Kushner/Greenblatt team. Despite all the talk of the “deal of the century,” the real deal – of the year at least – is Doha hoping it can finagle some kind of Gaza deal involving Egypt, Israel, Hamas and the US, with Turkey and Ramallah left out in the cold. Surely Turkey, today Qatar’s closest ally, will be concerned about that.