"There are preliminary dates. We expect to see representatives of the US president here in Kyiv," Zelenskiy said in his nightly video address.
"There will be a meeting with them in Moscow and in Kyiv. We are expecting a meeting with them in the coming days. It is very important."
Local officials said a Russian attack on the Ukrainian capital Kyiv on Thursday injured 10 people, triggered a fire and badly damaged a high-rise residential building.
The city's military administration initially said one person had died in the latest assault but later said the report had proved untrue.
It said 10 people, including a child, had been hurt.
Mayor Vitali Klitschko said nine people were injured, including six medical personnel.
Klitschko, writing on Telegram, said the ninth floor of a high-rise residence had been damaged.
Video published on unofficial Telegram channels showed a large fireball rising skywards.
Unofficial channels said the building had been struck by a jet-powered drone.
Klitschko said six people had been wounded in earlier strikes on the capital, which has been subject to more than a week of sustained attacks.
