"We want ground troops from Germany to partly replace our soldiers" in the area as part of the anti-IS coalition, US special representative on Syria James Jeffrey told German media including the Die Welt newspaper.
Jeffrey, who was visiting Berlin for Syria talks, added that he expects an answer this month.
Last year US President Donald Trump declared victory against IS and ordered the withdrawal of all 2,000 American troops from Syria.
But a small number have remained in northeastern Syria, an area not controlled by the regime of President Bashar al-Assad, and Washington is pushing for increased military support from other members of the international coalition against IS.
"We are looking for volunteers who want to take part here and among other coalition partners," Jeffrey said.
Washington has two goals in the region: to support the US-backed Kurdish forces that expelled IS from northern Syria as they are increasingly threatened by Turkey, and to prevent a potential IS resurgence in the war-torn country.
The US is hoping Europe will help, pressuring Britain, France and now Germany, which has so far deployed surveillance aircraft and other non-combat military support in Syria.
However Germany's history makes military spending controversial, so the prospect of sending ground troops may provoke division in Chancellor Angela Merkel's fragile coalition government.
The Social Democrats — the junior partner of Merkel's governing coalition -- are likely to oppose any suggestion of sending soldiers to Syria.
The US request comes after Trump has repeatedly urged Berlin to increase its defence spending, last month calling Germany "delinquent" over its contributions to NATO's budget.
Syria's war has killed more than 370,000 people and displaced millions since it started in 2011 with a brutal crackdown on anti-government protests.
