The Washington Post first reported that the call had taken place, citing unidentified sources and saying that Trump had told Putin that he should not escalate the Ukraine war.
Reuters also reported on the call, citing an unidentified source.
"This is completely untrue. This is pure fiction; it's just false information," Kremlin spokesman Dmitry Peskov told reporters. "There was no conversation."
"This is the most obvious example of the quality of the information that is being published now, sometimes even in fairly reputable publications," Peskov said.
Asked if Putin had plans for any contacts with Trump, Peskov said: "There are no concrete plans yet."
Five people were killed in a Russian drone attack on Mykolaiv in southern Ukraine, where a residential building and a house were destroyed, regional officials said on Monday.
In Zaporizhzhia, southeastern Ukraine, a Russian air attack injured five children between the ages of four and 17, according to regional officials.
The Ukrainian air force said it had shot down two missiles and 39 out of 74 drones launched by Russia overnight.
Officials also said that a Russian missile hit a residential building in Kryvyi Rih in central Ukraine, injuring at least seven people, with more trapped under the rubble.
Earlier in the day, Ukraine braced itself for a massive cruise missile attack after the air force put the country on high alert, warning that a large number of bombers were taking off from Russian territory for the first time in more than two months.
In anticipation of what the military expected to be a large-scale attack, Ukraine introduced precautionary power blackouts and urged people across the country to seek shelter. According to some reports, eight Tu-95s had taken off.
But by noon on Monday, no mass cruise missiles strike had been reported, leading some Ukrainian military bloggers to conclude that the Russian bombers had only performed maneuvers intended to mimic an impending attack.
Several regions and parts of Kyiv were without power earlier, and social media footage showed masses of people gathering in the city's metro stations—which have served as bomb shelters since the start of Russia's war in Ukraine in February 2022.