Trump’s communications director Steven Cheung told the BBC: “We do not comment on private calls between President Trump and other world leaders.”
But he said leaders have begun the process of contacting the president-elect.
Kremlin spokesperson Dmitry Peskov denied a conversation had taken place.
“This is completely untrue, it is pure fiction. That is, this is simply false information. There was no conversation,” Peskov said.
Russia’s denial comes days after Russia and Ukraine launched their largest drone attacks since the start of the war.
Russia’s defence ministry said it intercepted 84 Ukrainian drones over six regions, including some approaching Moscow, which forced flights to be diverted from three of the capital’s major airports.
Ukraine’s air force said Russia launched 145 drones towards every part of the country on Saturday night, with most shot down.
On Monday, at least six people were killed and 21 others injured in Ukraine following the latest series of air strikes by Russia.
Five were killed in the southern city of Mykolaiv and another was killed in Zaporizhzhia, authorities said.
Volodymyr Zelensky, Ukraine’s president, said that at least seven people including two children were hurt when an block of flats was hit by a missile in Kryvyi Rih, his home city in central Ukraine.
Russia, meanwhile, said it had destroyed 13 Ukrainian drones near the western regions of Kursk and Belgorod. It reported no deaths.