His comments give fuel to growing interest in a one-state solution as negotiations to create a sovereign Palestinian state have stalled in recent years.
Trump also called for an Arab-backed peace process -- an idea that's been periodically revived over the past two decades without producing results. But such a process insists on a sovereign Palestinian state.
Speaking to reporters Wednesday alongside Israeli Prime Minister Benjamin Netanyahu, Trump said he was "looking at two-state and one-state" solutions and that he could "live with either one."
"I thought for a while the two-state looked like it may be the easier of the two but honestly, if Bibi and if the Palestinians -- if Israel and the Palestinians are happy, I'm happy with the one they like the best," he said, referring to Netanyahu by his nickname.
But Trump toed the line on previous US administrations' stance on Israeli settlements, telling Netanyahu directly that he would like Israel to hold back on building more settlements homes "for a little bit."
Trump emphasized that he and Netanyahu had known each other for some time, calling him a "smart man" and a "great negotiator."
"I think we're going to make a deal. It might be a bigger and better deal than people in this room even understand. That's a possibility so let's see what we do," he said.
What is the two-state solution?
The idea of the two-state solution sounds simple enough -- an Israeli state next to a Palestinian state, existing side by side in peace.
But progress on the goal has been far from easy and has stalled in recent years. The most recent round of negotiations fell apart in April 2014 with Israeli and Palestinian leaders blaming each other. The two sides have failed to come to an agreement over several issues central to the solution.
Both claim parts, if not all, of the holy city of Jerusalem as their capital. They dispute where to draw borders and they continue to clash over Israeli settlements in occupied territory. In addition, what happens to the Palestinian refugees who fled what is now Israel after the 1948 war is a point of contention. The UN estimates that there are 700,000 Palestinian refugees in the world.
The two-state solution has been the goal of the international community for decades, dating back to the 1947 UN Partition Plan, and many nations say that it is the only way out of the conflict.
It would recognize a 1967 demarcation line known as the Green Line to partition Palestinian and Israeli land, subject to land swaps based on negotiations, and it would divide Jerusalem between the two states.
Netanyahu endorsed the idea of two states in 2009 under pressure from the Obama administration, but on Wednesday he sidestepped questions about whether he still supports it.
He said instead he wanted to avoid "labels" and talk "substance" -- the need for Palestinians to recognize Israel as a Jewish state and the need for Israel to have overriding security control.
Many in his right-wing government are celebrating his comments, seeing it as an end to a future Palestinian state, calling for more construction of settlement homes and some even calling for a partial or full annexation of the West Bank.
What would a one-state solution look like?
From Israel's perspective, a one-state solution means it would annex either part or all of the West Bank and Gaza.
But this forces Israel to make a decision, since there are approximately an equal number of Jews and Arabs throughout Israel, the West Bank, and Gaza. If Israel gives Palestinians a right to vote, then Jews would soon be a minority, since the Arab population is growing faster as a demographic than the Jewish population.
If Israel doesn't give Palestinians the right to vote, Israel would remain a Jewish state but would no longer be a democracy. Israel's critics say it would become an apartheid state, with one set of rights for Israelis and another set for Palestinians.
Why are settlements a problem?
Recent announcements by the Israeli government of the expansion of West Bank settlements,
made in the period since Trump became president, have put settlements back in the spotlight. The announcements came just weeks after the UN Security Council Resolution declared that settlements had "no legal validity."
Settlements are Israeli cities, towns and villages in the occupied West Bank, the Golan Heights and East Jerusalem. They are considered settlements and not Israeli residential areas because Israel is widely considered to be an occupying force in the territories. It is land that Palestinians, along with the international community, view as territory for a future Palestinian state.
Just before finishing his term as US Secretary of State, John Kerry said Israel's settlement policy was leading to a future of "one state and perpetual occupation" He slammed the arguments of right-wing Israeli officials who claim settlements are aimed at bolstering Israel's security.
Who would support one state?
Virtually the entire international community supports a two-state solution. In the Middle East, most countries support the 2002 Arab Peace Initiative, put forward by Saudi Arabia. The initiative was adopted unanimously by the Arab League.
But there are militant factions that reject Israel's right to exist and support a one-state solution -- but one called Palestine, not Israel. Hezbollah in Lebanon and Hamas in Gaza have both called for the destruction of Israel.
Many in Israel's right-wing support a one-state solution -- they envisage that state as a Jewish state. While some are willing to give the Palestinians full citizenship and equal rights, others would confer upon the Palestinians a lesser autonomy. Palestinians, who have their own national aspirations, criticize the latter system as akin to apartheid.
Many Israelis and Palestinians on the far-left -- as well as far-left Europeans and Americans -- also support a one-state solution, but in a very different form. They envision a secular state for all citizens, regardless of religion, culture or ethnicity. Most Israelis recoil at this idea because it's seen as removing the Jewish character of the country and a way of eliminating the state of Israel by non-military means.
Some Palestinians who prefer the one-state solution are frustrated with the failure of the Oslo Peace Accords and see no hope in continued peace negotiations. They feel the international community is not taking concrete steps in changing the reality after nearly 50 years of Israel's military occupation of the West Bank. They would rather force Israel to take full responsibility for security in the West Bank, as was the case before the Oslo accords.