Foreign ministers from the two powers, which support opposite sides in the five-year conflict, were poised to hold a "personal meeting" in the Swiss city to push for a peace agreement, according to the Russian side.
However, Washington did not confirm the face-to-face talks, with a spokesman for US Secretary of State John Kerry saying that negotiations were still ongoing.
And US Defense Secretary Ash Carter told BBC radio today there was "quite a long way to go" before a final deal could be struck.
Both sides have agreed that a deal would involve a durable ceasefire, humanitarian access to conflict-wracked areas and a resumption of peace talks.
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The Syria war has pitted the old Cold War rivals against each other, with Russia flying a bombing campaign in support of Syrian strongman leader Bashar al-Assad and the United States backing rebel groups fighting to oust him from power.
US President Barack Obama held talks with his Russian counterpart Vladimir Putin on the sidelines of the G20 summit in China but failed to bridge their differences.
And Carter noted: "We have our differences, serious differences, with Russia elsewhere, especially here in Europe with Ukraine and elsewhere Russia has been acting in an aggressive manner."
As diplomatic efforts intensified, fighting in the complex war continued to claim lives, with Turkish shelling over the border into Syria killing six US-backed Kurdish fighters.
Pro-regime forces also overran a strategically important district on the southern outskirts of Aleppo today, rolling back nearly every gain from a major month-long rebel offensive there, said the Syrian Observatory for Human Rights.