The comments were made in an Ukrainian documentary called Year, according to The Times.
It comes as the Russian leader Mr Putin warned his people that they might not survive as a nation if Ukraine wins the war.
Mr Zelensky told the documentary: “There will definitely be a moment when the fragility of Putin’s regime will be felt inside the [Russian] state.
“And then the predators will devour a predator. They will find a reason to kill a killer.”
Analysts have said however that it is unlikely that the hardliners in Mr Putin’s inner circle would move against him as they owe their positions to him.
Mr Putin has recently claimed that he has no choice but to take Nato’s nuclear capabilities into account and accused the US-led military alliance of wanting to “disband the former Soviet Union and Russia”.
Mr Zelensky on Sunday expressed his confidence that the return to Ukrainian control of the Crimean peninsula would be part of an end to the war.
He wrote on Twitter: “This is our land. Our people. Our history. We will return the Ukrainian flag to every corner of Ukraine.”
The head of the CIA has said that Mr Putin is being “too confident” in his military’s ability to grind Ukraine into submission. William Burns said that Mr Putin has a belief that “he can make time work for him, that he believes he can grind down the Ukrainians, that he can wear down our European allies, that political fatigue will eventually set in”.
In conversation with CBS’ Face the Nation, Mr Burns added: “At some point, he’s going to have to face up to increasing costs as well, in coffins coming home to some of the poorest parts of Russia.”
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