Abbas and Trump spoke for the first time in March, when he invited the Palestinian President to the White House. The US President expressed his desire to reach the "ultimate deal:" peace between the Palestinians and Israelis.
Officials in Ramallah describe Abbas as hopeful and eager to engage Trump. "I am ready to meet the Prime Minister of Israel any time in Washington under the patronage of President Trump," the Palestinian President told the Japanese Asahi Shimbun newspaper in April.
And his aides see at least some reason to think that Trump offers a fresh approach that could see progress.
"The difference with President Trump is that he himself and the White House is engaged. It's not the State Department," said Mohammed Shtayyeh, Fatah Central Committee member and presidential adviser. "We now feel that the file itself is in the White House, which gives a very serious political weight for any American initiative because it's the American President's reputation at stake."
Then there is Trump's policy, which is also different from that of his predecessors -- in some cases drastically so -- but in ways many Middle East observers don't see as likely to produce a deal.
Trump breaks with precedent
Trump broke from decades of American tradition at a White House news conference alongside Israeli Prime Minister Benjamin Netanyahu on February 15.
"I'm looking at two-state and one-state, and I like the one that both parties like ... I can live with either one," Trump told reporters. Previous peace deals focused on two states, Palestinian and Israeli, living side by side. A Palestinian state is widely expected to be within the 1967 border, including land swaps, and the status of Jerusalem finalized through negotiations.
Don't expect the majority of Palestinians to "like" a one-state solution, which they expect would expand Israeli control of the contested territory. Most Israelis are opposed to it as well, believing that Palestinian demographics would eventually erase the Jewish character of their state.
But there are factions that favor it, particularly among the Israeli right wing, and by dangling out the prospect of such a change, Trump displayed his willingness to deviate from the orthodoxy about how to conduct a peace process, one that has so far failed to resolve the conflict.
Trump has appointed diplomatic novices to key positions in the peace mission, including giving a central role to his son-in-law Jared Kushner, who, like Trump, is a real estate developer. The President also tapped New York bankruptcy lawyer David Friedman as the new US ambassador to Israel, and dispatched as a Middle East envoy Jason Greenblatt, who was once a lawyer at Trump's business.
Palestinians wary of US ambassador
Palestinians reacted negatively to the announcement of Friedman. The jury is still out on Greenblatt. After his first meeting with the new Middle East emissary, Shtayyeh described Greenblatt as a man who listens while not saying much in return.
"Greenblatt is an envoy of the White House, all others were envoys of the State Department," recalls Shtayyeh. "He seems to be a very capable lawyer and, on the other hand, he is stationed in the White House. Therefore that makes his voice directly to the ear of the President and I think that's a real added extra value for Greenblatt."
Trump also adopted controversial positions during the presidential campaign that alarmed Palestinians, particularly pledging to move the US Embassy from Tel Aviv to Jerusalem.
But since taking office, and following criticism from foreign policy hands and officials in the Arab world, the issue has appeared to have been pushed aside -- though Vice President Mike Pence said at an Israeli Independence Day celebration Tuesday night that his boss was still giving "serious consideration" to the move. The White House has been warned about the broader implications such a decision could have in the region.
"President Trump has made some promises, and we hope he doesn't fill them, including moving the embassy," said Shtayyeh, who noted that Abbas would bring up the issue at their meeting.
Another crucial issue for Palestinians is settlements. Trump has been more open to allowing Israel to build in the West Bank than President Barack Obama was, and that openness was greeted with Israeli moves to take advantage of the change.
Early into Trump's presidency, Israel announced thousands of new settlement housing units and its first entirely new settlement in decades. Recently, Israel's Housing Ministry revived a plan for at least 10,000 new homes in East Jerusalem, which Palestinians claim for their future capital. The plan was previously shelved after strong opposition from the Obama administration.
But, as with the embassy move, Trump has gradually modified his tone. After his meeting with Netanyahu in February, he called on the Israeli leader to "hold back on settlements for a little bit," and the administration later called the building unhelpful for peace efforts.
"For us, the most important test for any American administration is whether they can deliver Netanyahu on freezing settlements," said Shtayyeh. "This is the barometer for a successful peace administration or not."
Settlement freeze coming?
A settlement freeze would be difficult for Netanyahu. His government is filled with right-wing politicians, many of whom have ties to the settler movement. Friedman is also a staunch defender of settlements.
"I would like to have hopes that this will bring some constructive new thing, but I'm very doubtful," said Palestinian politician Mustafa Barghouti. "Does Mr. Trump have the ability or the willingness to pressure Mr. Netanyahu? Netanyahu has a very extreme government and he is not capable to be a peace partner."
Netanyahu spoke about the prospects for peace to Fox News' Sean Hannity last month, saying, "I know the cost of war. There's no one that wants peace more than Israel. This canard that Israel doesn't want peace, that I don't want peace, is exactly that. It's a canard. It's a joke."
He added that the Palestinians are the ones who need to be pressed for a deal to happen. "We don't have double talk because what we say inside is what we say outside, and everybody holds us accountable," he said. "It's high time that that accountability was put on the Palestinians."
There are moves the US government is looking for Palestinians to make in order to bridge gaps with the Israelis, such as ending incitement against Israel.
He, too, has a precarious political position. The Palestinian extremist group Hamas threatens the hold that Abbas' Fatah party has on the Palestinian Authority's West Bank territory. The militant organization, which has fought three wars with Israel in the past nine years, wrested control of Gaza from Abbas in 2007 .
Before a peace deal can be realized, Palestinian factions Hamas and Fatah have to reconcile in order to form a shared agreement. Fatah and Hamas have tried in vain to bridge their differences over the past decade. Hamas, designated a terror group by the United States and Israel, is all but sure to come up during Abbas' visit.
On Monday night, the group announced its new charter. Key changes include the acceptance of a Palestinian state within the 1967 border with Jerusalem as its capital as a "consensus" position. It also states Hamas's desire to be a part of the Palestinian political process with the PLO and Palestinian Authority. But Hamas continued to refuse to recognize the legitimacy of Israel and to back violence to oppose its existence.
It's yet to be seen how this change will affect the upcoming White House visit. But when it comes to reconciliation between the two sides, Barghouti believes it's a positive step. "It's about accepting the two-state solution on '67 borders, including Jerusalem, and this practically makes it easier for Palestinians to be unified on one program," he said.
But neither Hamas nor Fatah seems to be eager to acquiesce. Hamas spokesman Fawzi Barhoum criticized Abbas' visit in a press statement on Monday.
"Any bet on the meeting of Palestinian Authority President Mahmoud Abbas with US President Trump in achieving any achievements for the benefit of our people and his case is a wasteful, time-wasting and marketing illusion," he said.