The statement comes after US envoys Steve Witkoff and Jared Kushner visited both Moscow and Kyiv this past weekend.
"We do not rule out the resumption of trilateral cooperation, but it is too early to say anything about the location or exact dates at this stage," said Kremlin spokesman Dmitry Peskov.
Ukrainian President Volodymyr Zelenskyy stressed on Sunday that talks with the US envoy had been positive, although he said he did not see a quick end to the war.
Witkoff said in connection with the approximately three-hour meeting in Kyiv that both Ukraine and Russia must be prepared to compromise.
Later on Monday, an official in the French presidential staff said that US envoys Witkoff and Kushner had interpreted "new willingness to negotiate" in the Kremlin after their visit to Moscow on Saturday.
The Americans told us that there is a new willingness on Russia's part to negotiate after the Duma (parliament) elections, and that we should prepare for a new start in the negotiations, the official said.
Kushner and Witkoff met with representatives from France, Britain and Germany in a separate meeting after this weekend's round of negotiations.
Russia's parliamentary elections will be held on September 18-20. Elections in Russia are not considered democratic.
