According to Podolyak, the Ukrainian government has "operation information" about attempts by Russians to kill the president.
He also said that hit squads are "still being eliminated".
Multiple sources say the Wagner Group mercenaries have been in Ukraine since January and are tracking Zelenskyy and his colleagues via their cell phones.
Zelenskyy is said to not be fazed by the assassination attempts and remains defiant and determined to keep fighting for Ukraine.
The President has refused to leave Kyiv even when offered help to get out by the US, in the early days of the war.
"I need ammunition, not a ride," he told US President Joe Biden at the time.