Mustafa Bali, head of the SDF media office, did not indicate how soon he expected the civilian evacuation to be completed.
In December, Trump declared victory over the Islamic State terror group in war-torn Syria and announced that American forces would be "coming home soon", sparking concern among officials in Washington and allies overseas.
Bali did not say how long they expect the battle to last.
USA officials have said in recent weeks that ISIS has lost 99.5 percent of its territory and is holding on to fewer than five square kilometres in Syria in the villages of the Middle Euphrates River Valley, where the bulk of the fighters are concentrated.
"There hasn't been any big advance or change on our side over the past 5 days", an SDF spokesman told Agence France-Presse (AFP) on Friday.
In December 2018, Turkish President Recep Tayyip Erdogan said that Ankara's armed forces were ready to initiate a campaign in eastern Syria if the USA didn't remove its Kurdish allies from the region.
IS overran large parts of the country and neighboring Iraq in 2014, declaring a "caliphate" there, but various military offensives have reduced it to a fragment.
In recent days, President Trump has said the total defeat of IS could be declared next week.
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At the height of its rule, IS controlled territory the size of Britain. A series of assaults have left that proto-state in tatters.
Major General Christopher Ghika, the coalition's deputy commander, described the size of the last IS pocket as "now less than one percent of the original caliphate".
The conservative chancellor said monitoring events in Syria was one of the BND's top priorities, which also include tracking cyber threats and fake news created to influence democratic elections.
The Kurds, who have de facto autonomy in northeastern Syria, are also engaged in behind-the-scenes diplomatic talks over the fate of the region.
Speaking at the State Department on Wednesday, Trump said that US-led troops and their Kurdish allies should formally announce the end of the "caliphate" some time next week.
The Kurdish People's Protection Units (YPG) have formed the backbone of the US-backed SDF, but neighbouring Turkey sees them as "terrorists". According to The Wall Street Journal, the military plans to complete the withdrawal of all United States troops from Syria by the end of April.
The December announcement of a U.S. troop pullout from Syria has seen Kurdish authorities scrambling to mend fences with the regime in Damascus.