A motorcade carrying Witkoff, Kushner and Dmitriev left Moscow's governmental airport on Saturday and headed towards the city, a Reuters witness said.
Russian spokesman Dmitry Peskov told TASS news agency President Vladimir Putin would meet Witkoff and Kushner in the Kremlin later on Saturday.
US President Donald Trump suggested on Friday the US had a fresh concrete proposal aimed at ending the war, which is now in its fifth year.
He did not, however, elaborate on what that proposal would be.
Russian envoy Dmitriev, who told Reuters in June he had remained in contact with the US negotiators during a pause in their visits to Russia, took part in all their previous meetings with Putin alongside Putin's foreign policy aide Yuri Ushakov.
He also played a role in negotiating US sanction waivers for Russian oil this year.
Ukrainian President Volodymyr Zelenskiy said on Friday the two men would fly to Ukraine on Sunday after visiting Moscow.
In a post on X on Saturday, Zelenskiy said Russia hit two Ukrainian airports ahead of US envoys' visit to Kyiv.
Peskov said in a statement posted on the Kremlin's channel in Max messenger that Putin had ordered the military not to strike Kyiv for three days, starting at midnight on Saturday, in connection with Witkoff and Kushner's visit to the Ukrainian capital.
The Russian Defence Ministry reported 53 Ukrainian drones in Russian airspace on Saturday, significantly fewer than the average seen in recent months.
Moscow is celebrating City Day on Saturday, with hundreds of thousands of people taking part in open-air festivities across the city.
A vast gulf remains between Russia and Ukraine on how to end the more than four-year-old war, the deadliest in Europe since World War Two.
A source close to the Kremlin, speaking before reports emerged of a possible trip by President Trump's envoys, said Putin was still intent on capturing more territory.
"There is no chance of reaching an agreement regarding the front line until Putin finishes securing the remaining part of the Donetsk region," the source told Reuters, adding that the Kremlin leader was confident - based on reports from his commanders - that this would happen by the end of the year.
Western military analysts see such a possibility as remote, given Moscow's slow rate of progress.
Ukraine refuses to surrender land that it has successfully defended at huge cost, and rejects such terms as tantamount to surrender.
The Kremlin said on Friday 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".
Since the last peace talks in February, each side has intensified long-range air attacks deep inside the other's territory, while the war at sea has also escalated.
On the ground, the front lines have remained largely static, with Russia making only gradual gains in its attempt to take the whole of Ukraine's Donbas region.
Ukraine's drone strikes on Russian oil refineries have led to a summer of fuel shortages and rising prices for Russian motorists, while some 30 attacks on giant warehouses belonging mostly to Wildberries, the country's biggest online retailer, have affected the consumer economy.
A Russian drone attack hit the headquarters of Ukraine's SBU security service in Kyiv on Friday - the 10th consecutive day of heavy attacks on the capital - and Zelenskiy vowed to retaliate.
with AP
