Russian state news agency TASS reported American negotiators Steve Witkoff and Jared Kushner would visit Moscow first, then Kyiv on September 5-6.
TASS did not identify its source.
US officials did not immediately confirm the visit.
President Donald Trump's envoys, Witkoff and Kushner, last visited Moscow in January, when they held four hours of late-night talks with President Vladimir Putin in the Kremlin.
"I wouldn't make any announcements right now, but we will inform you when these contacts take place," Kremlin spokesman Dmitry Peskov told reporters when asked about the TASS report.
Witkoff and Kushner have yet to visit Ukraine, but President Volodymyr Zelenskiy said on Thursday that Trump's representatives were expected in Moscow and Kyiv in the coming days.
A source familiar with the matter told Reuters that discussions on the Ukraine part of the trip were still taking place, and the teams had spoken about Sunday as a possible date.
"The Russians don't want them to visit Kyiv and are trying to make them change the plan," the source added.
A vast gulf remains between Russia and Ukraine on how to end the four-and-a-half-year-old war, the deadliest in Europe since World War II.
Peskov said the position that Putin set out in a speech two years ago - that Ukraine should cede the entire territory of four regions claimed by Russia and abandon its plan to join NATO - was "unshakeable".
Ukraine refuses to surrender land that it has successfully defended at huge cost, and rejects such terms as tantamount to surrender.
Putin said on Thursday there was a chance of reaching an agreement to end the war in Ukraine. But he added that Kyiv's warning to foreign airlines this week to avoid Russian airspace amounted to a threat that would make talks more difficult.
The last US-mediated talks between Russia and Ukraine took place in February, shortly before the United States and Israel launched a war against Iran.
Peskov said the possibility of eventually reaching a peace settlement could not be ruled out, but the necessary basis for this did not exist right now.
"The work continues, and the contacts continue," he said.
On the battlefront, one of the World Health Organization's main warehouses storing humanitarian medical supplies in Ukraine was struck during an air attack overnight in the region surrounding Kyiv, the WHO said.
"Access to the site remains restricted due to heavy smoke and safety concerns, while assessments of possible damage and stock losses are ongoing. No WHO personnel were affected," WHO spokesperson Christian Lindmeier said.
The attack follows a strike in August on a WHO humanitarian warehouse in the southern city of Dnipro, resulting in the loss of half of the medical supplies and equipment intended to support an estimated 225,000 people living in front-line and hard-to-reach areas, according to the WHO.
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