"We want to see if we can bring that war to an end," Trump told reporters on Air Force One during a flight back to the Washington area from Florida.
"Maybe we can, maybe we can't, but I think we have a very good chance.
"I'll be speaking to President Putin on Tuesday. A lot of work's been done over the weekend."
Trump is trying to win Putin's support for a 30-day ceasefire proposal that Ukraine accepted last week, as both sides continued trading heavy aerial strikes through the weekend.
Russia is moving closer to ejecting Ukrainian forces from their months-old foothold in the western Russian region of Kursk.
Asked about what concessions are being considered in ceasefire negotiations, Trump said: "We'll be talking about land. We'll be talking about power plants ... We're already talking about that, dividing up certain assets."
Kremlin spokesman Dmitry Peskov confirmed Putin would talk to Trump by phone on Tuesday.
The Kremlin earlier said on Friday that Putin had sent Trump a message about his ceasefire plan via US envoy Steve Witkoff, who held talks in Moscow, expressing "cautious optimism" that a deal could be reached to end the three-year conflict.
In separate appearances on Sunday TV shows in the United States, Witkoff, Secretary of State Marco Rubio, and Trump's national security adviser, Mike Waltz, emphasised there were still challenges to be worked out before Russia agrees to a ceasefire, much less a final peaceful resolution to the war.
Asked on US broadcaster ABC whether the US would accept a peace deal in which Russia was allowed to keep stretches of eastern Ukraine that it has seized, Waltz replied, "Are we going to drive every Russian off of every inch of Ukrainian soil?"
He added that the negotiations had to be grounded in "reality".
Rubio told CBS a final peace deal would involve "concessions from both Russia and Ukraine", and that it would be difficult to even begin those negotiations "as long as they're shooting at each other".
An overnight Ukrainian drone attack targeted energy facilities in Russia's southern Astrakhan region, injuring one person and sparking a fire, the regional governor said.
Kyiv's mayor said on Monday Russia had carried out an overnight drone attack on the Ukrainian capital.
Ukraine's President Volodymyr Zelenskiy said on Friday he saw a good chance to end the Russian war after Kyiv accepted the US proposal for a 30-day interim ceasefire.
However, Zelenskiy has consistently said the sovereignty of his country is not negotiable and that Russia must surrender the territory it has seized.
Russia seized the Crimea peninsula in 2014 and now controls most of four eastern Ukrainian regions since it invaded the country in 2022.
Russia will seek "ironclad" guarantees in any peace deal that NATO nations exclude Kyiv from membership and that Ukraine will remain neutral, a Russian deputy foreign minister said in remarks published on Monday.
In an interview with the Russian media outlet Izvestia that made no reference to the ceasefire proposal, Deputy Foreign Minister Alexander Grushko said any long-lasting peace treaty on Ukraine must meet Moscow's demands.
"We will demand that ironclad security guarantees become part of this agreement," Izvestia cited Grushko as saying.
"Part of these guarantees should be the neutral status of Ukraine, the refusal of NATO countries to accept it into the alliance."
The European Union's foreign policy chief, Kaja Kallas, said on Monday that the conditions demanded by Russia to agree to a ceasefire showed that Moscow does not really want peace.
British Prime Minister Keir Starmer said on Saturday that Western allies other than the US were stepping up preparations to support Ukraine in the event of a ceasefire with Russia, with defence chiefs set to firm up "robust plans" next week.
