About 500 US troops are in Syria in support of the campaign against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS).
The US-led coalition is currently backing a campaign by its Syrian militia allies to encircle and ultimately capture Raqqa, ISIL's base of operations in Syria.
Assad, in an interview with Chinese TV station Phoenix that was published by Syria's state television SANA on Saturday, said Trump's "rhetoric" has not resulted in "anything concrete yet".
"We have hopes that this administration in the United States is going to implement what we have heard," he said.
Asked about a deployment of US forces near the northern city of Manbij that is held by US-backed rebels, Assad said: "Any foreign troops coming to Syria without our invitation ... are invaders. We don't think this is going to help."
Assad dismissed the US-backed military campaign against ISIL in Syria as "only a few raids", and said a more comprehensive approach was needed.
The president noted the Russian-backed Syrian army was now "very close" to Raqqa city after advancing to the western banks of the Euphrates River this week - a rapid gain that has brought it to the frontier of areas held by US-backed forces.
He said Raqqa was "a priority for us", but indicated there could also be a parallel army attack towards Deir Az Zor province - almost completely controlled by ISIL - in the east, near the Iraqi border.
The Deir Az Zor region had been "used by ISIS as a route for logistics support between ISIS in Iraq and ISIS in Syria, so whether you attack the stronghold or you attack the route that ISIS uses, it [has] the same result", Assad said.
He also spoke about UN-led peace talks in Geneva that ended earlier this month with no breakthrough.
Assad said he had not expected anything from Geneva, adding deals brokered locally with rebels were "the real political solutions" since the war began.
Local "reconciliation" agreements are the government's preferred method for pacifying rebellious areas and have often been concluded after years of government siege and bombardment.
In some cases, opposition fighters have been given safe passage to the rebel-dominated province of Idlib. The opposition says the agreements amount to forced displacement.
"We didn't expect Geneva to produce anything, but it's a step and it's going to be a long way," Assad said.
He also said it would be up to Syrians to decide their future political system, and there would be a referendum on it.
Staffan de Mistura, the United Nations special envoy to Syria, estimated in April 2016 that more than 400,000 Syrians had been killed since the war started.
Calculating a precise death toll is difficult, partially owing to the forced disappearances of tens of thousands of Syrians whose fate remains unknown.
Almost 11 million Syrians - half the country's prewar population - have been displaced from their homes.
Source: News agencies