That's according to Ukrainian MP Yuriy Kamelchuk, a member of Zelensky's Servant for the People party.
Kamelchuk said he received information from advisers to the Ukrainian presidential office that Putin and Zelensky could meet for talks in Israel, with a date expected to be set soon.
"It is possible to provide negotiations in Israel," he said. "We have additional information from our diplomacy that in maybe two or three days we will have a result of the date for those negotiations between Zelensky and Putin. First we need agreement for those negotiations and also a date - when it can be possible."
Israel has become the likeliest mediator in peace talks due to its good relations with both Ukraine and Russia. Israeli Prime Minister Naftali Bennett has met with Putin in Moscow and held phone calls with Zelensky in an attempt to get the two leaders talking.
In a press conference at the weekend, Zelensky praised Bennett's efforts to broker peace.
"We have a positive stance on the mediation efforts… we believe that he can play an important role, because Israel is a special country with a lot of history and a lot of parallels, and Israel also underwent a large wave of migration of Jews from Ukraine, Russia, Belarus, and all of Europe," he said. "I believe it’s not right to meet in Belarus, Russia or Ukraine, these are not places where we can find any understanding to stop the war. Maybe Israel could be such a country, especially Jerusalem. This is what I told (Mr Bennett)."
"Our diplomats are discussing details with Russia, and I hope that we will have a real peace process to end the war, but first there should be a ceasefire," he added. "This will allow us to open humanitarian processes, evacuation of people, and the delivery of water, food and medicines. We’re waiting for this process, we’re discussing processes to end this war. I’m happy in principle that we have received a signal from Russia. They hoped to occupy our country in three to four days, but unless they bring millions of Russians here to die, you cannot occupy Ukraine. You can lay siege to our cities, you can pepper Ukraine with the bodies of Russian soldiers, but you cannot occupy the minds of our people."
