According to an upcoming book by reporter Bob Woodward, Trump wanted to kill al-Assad after he launched the chemical weapons on civilians past year.
The Syrian military has been urging the rebels in Idlib to surrender.
Iranian television reported that the three leaders would each have "bilateral meetings" on the sidelines of the main summit.
Forces loyal to President Bashar al-Assad, often backed by Russian warplanes, have steadily gained on the rebels.
Just today, Russian President Vladimir Putin, Turkish President Recep Tayyip Erdogan, and Iranian President Hassan Rouhani met in Tehran, where Rouhani said the next step in Syria strategy was "to force the United States to leave".
Instead, Putin warned militants in Idlib planned "provocations", possibly including chemical weapons.
Although America has some 2,000 troops and outposts in Syria, Trump has said he wants to pull those forces out after the war against the Daesh group dislodged the extremists from vast territories it once held there and in Iraq.
The attacks were carried out after the USA government urged the Syrian government, which is assisted by Russian Federation and Iran in its civil war, not to attack the rebel stronghold where approximately 3 million people live. Previously, Trump "resisted significant involvement" in the Syrian civil war "even as both Iran and Russian Federation increased their influence", notes the Post.
China Pledges Fresh $60 bln to Africa, says No Political Strings Attached
Chinese companies were also encouraged to make at least US$10 billion in investment in Africa in the next three years, Xi said. He adds that this was not the only reason why the trip has been a success and why Ramaphosa is in China.
Hossein Jaberi Ansari, a senior aide in the Foreign Ministry, said the presidents would seek a compromise and that "Turkey and Iran are sufficiently mature politically to facilitate such a compromise".
The summit between Hassan Rouhani, Vladimir Putin and Recep Tayyip Erdoğan on Friday may determine whether diplomacy halts any military action.
Erdogan continued by saying that a rational solution in Idlib that will address everyone's concerns needs to found.
Turkish proposals also included creating a safe corridor for fighters who hand their weapons over to the Turks to move to a buffer zone controlled by the Syrian opposition.
The outcome of the meeting will be closely watched by the U.S.
"I don't think that either of these countries, or really anyone, has an interest in doing something which is genuinely destabilising to Turkey", he added. The Turks are trying to find a way out. An estimated 10,000 Al-Qaeda-linked fighters are among those rebels, and Idlib is also home to about 3 million civilians - almost half of them displaced from other parts of Syria.
Jeffrey warned of the risks of an offensive on the province and said the USA wouldn't "tolerate an attack (on Idlib), period!"
Russia, which has been building up forces in the region, said it's only targeting al-Qaeda fighters, and accused the US of preparing to fake a chemical attack to justify new intervention.
They destroyed one Ahrar al-Sham post, killing one of its fighters and wounding 14 others in the area of Hobait, it said.