Ukraine is hoping to secure the release of dozens of prisoners, including 24 sailors who were detained by Russia in the Kerch Strait last year, and filmmaker Oleg Sentsov.
"The process of the prisoner swap is ongoing. Information that it has been completed is untrue," the president's office said in a statement. Russia's Interfax news agency also cited a source in Moscow denying that an exchange had taken place.
Ukraine's general prosecutor had earlier reposted a comment on Facebook that the sailors and Sentsov were flying back from Russia after a prisoner swap had been completed.
Russia had transferred Sentsov from a remote Arctic prison to custody in Moscow amid talks with Kiev on a possible prisoner swap, news agencies TASS and Interfax reported on Thursday.
A Ukrainian court also freed a senior Russian journalist accused of supporting pro-Russian separatists.
Securing a prisoner swap would be a win for Zelenskiy, who became president this year promising to bring an end to the conflict in eastern Ukraine.
Ukrainian troops have been battling Russian-backed forces in the Donbass region of eastern Ukraine since 2014, in a conflict that has claimed more than 13,000 lives. Sporadic fighting continues despite a ceasefire agreement.
Russia is holding dozens of Ukrainian captives from the conflict. Oleksandr Danylyuk, a top Ukrainian security official, told Ukrainian media he hoped the prisoner swap might happen on Friday, but added:
"We have to wait for the exchange and then comment."