Putin has previously said that Zelenskiy is not a legitimate leader because he has remained in office beyond the end of his elected term.
Ukrainian law forbids the holding of new elections under martial law, which was imposed after Russia's 2022 invasion.
Putin told foreign journalists in St Petersburg that if it came to a peace deal, Russia would sign an agreement with legitimate Ukrainian representatives, perhaps "even with Zelenskiy".
Putin also said on Thursday that Russia will strengthen its air defences to counter recent Ukrainian drone attacks, which have reached deep inside his country.
He acknowledged the damage Ukrainian drone attacks had caused.
"To our regret, some of them break through," Putin said of the drone strikes on his hometown of St Petersburg.
"Russia has an air defence system, we need to improve it, strengthen it and we will do that."
Putin said that Russia is open for a compromise on Ukraine in line with understandings reached during his summit with US President Donald Trump in Alaska, adding that Ukraine needs to accept them to make a deal.
with AP
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