But while Trump said the United States has things "under control," a massive bombing in Kabul highlighted the rampant violence still plaguing Afghanistan and the major challenges it would face even if an agreement is reached.
"We're having very good discussions with the Taliban. We're having very good discussions with the Afghan government," Trump told reporters.
Expectations are rising for a deal in which the United States would start withdrawing its soldiers from Afghanistan after nearly two decades of war that has ground into a stalemate.
"We've really got it down to probably 13,000 people and we'll be bringing it down a little bit more and then we'll decide whether or not we'll be staying longer or not," Trump said.
"We have things under control very well with the small force. We can probably make it a little bit smaller and then we'll decide," he said, adding: "It'll depend on the Taliban, it'll depend on the Afghan government."
A US-Taliban agreement would not by itself bring an end to Afghanistan's war, as the insurgents would still need to make a deal with the Washington-backed government in Kabul.
Trump reiterated Sunday that the United States would maintain an intelligence presence in the country even if it withdraws troops, in order to guard against potential militant threats.
"I think it's very important that we continue intelligence there in all cases, because it is somewhat of a nest for hitting us," the US president said.
Washington is keen to end its involvement in Afghanistan, where it has spent more than $1 trillion and Trump has said since the start of his presidency that he wants troops out.
In return, the Taliban would commit to various security guarantees, including that the hardliners who long harbored Al-Qaeda would not allow Afghanistan to become a militant safe haven - but any such promise would be tough to keep.
On Saturday, a bombing at a packed Afghan wedding hall killed at least 63 people, underscoring both the inadequacy of Afghanistan's security forces and the massive challenges they face.
The Islamic State militant group claimed the attack, saying that one of its fighters blew himself up at a "large gathering" in Kabul while others "detonated a parked explosives-laden vehicle" when security forces arrived.
While the Afghan police and army claim they prevent most bombings from ever happening, insurgents pull off horrific attacks with chilling regularity.
And even as Trump claimed progress in talks, little has changed for Afghans on the ground.
A UN tally found last year was the deadliest on record, with at least 3,804 civilian deaths caused by the war - including 927 children. And according to the UN's Office for the Coordination of Humanitarian Affairs (OCHA), more than 217,000 people had to flee their homes because of fighting during the first seven months of 2019, prompting a huge need for humanitarian aid across the war-torn nation.
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