Contacts between Russia and the United States are now quite intensive, Russian Foreign Ministry spokeswoman Maria Zakharova was quoted as saying by the RIA news agency on Tuesday.
Zakharova was commenting on media reports that Trump's special envoy Steve Witkoff plans to visit Moscow this week to meet President Vladimir Putin.
Witkoff, who is officially Trump's Middle East envoy, has played a growing role in efforts to bring about an end to the three-year-old Ukraine war.
The people, speaking on condition of anonymity, confirmed a Bloomberg News report that Witkoff would be going to Moscow for talks with Putin.
One of the sources said Witkoff is expected to travel to Moscow this week.
Trump has expressed a desire to meet Putin and, since taking office in January, has pursued an effort to reverse the icy relations with Russia of the previous Biden administration.
Witkoff met Putin in Moscow last month and brought back American schoolteacher Marc Fogel, who had been sentenced to 14 years in a Russian prison after being detained for holding medically prescribed marijuana.