But the Kremlin leader struck a hardline tone, warning the West it was an "illusion" to think Russia could be defeated on the battlefield and that any peace deal would have to recognise Russia's control of swathes of Ukrainian territory.
Putin was speaking at the end of the BRICS summit in the city of Kazan, where he had faced calls from some of Russia's most important allies for the fighting in Ukraine to end.
"How Russian-American relations will develop after the election will depend on the United States. If they are open, then we will also be open. And if they don't want it, then fine," Putin told reporters in Kazan.
Relations between the two superpowers have sunk to their lowest since the Cold War amid Moscow's military offensive on Ukraine.
Next month's US election is set to be critical in the course of future ties and the conflict in Ukraine. Trump has repeatedly expressed scepticism over Washington's multi-billion dollar aid to Ukraine and claimed that if elected he could end the fighting in a matter of hours.
Putin said Trump "spoke about his desire to do everything to end the conflict in Ukraine. I think he is being sincere. Of course we welcome statements like this, whoever they come from." Chinese President Xi Jinping and Indian Prime Minister Narendra Modi were among around 20 leaders that gathered for the BRICS summit, the largest diplomatic event in Russia since Putin ordered troops into Ukraine in February 2022.
The Kremlin leader said Moscow was open to considering peace initiatives and welcomed BRICS leaders offering to mediate.But he said any deal must consider the "realities on the ground" -- a reference to Ukrainian territory controlled by Russian forces. "We are ready to look at any proposals for peace negotiations that are based on the realities on the ground. We won't accept anything else," he said.
Putin has previously demanded Kyiv effectively capitulate by pulling its troops back as a precondition to ceasefire talks. And on Thursday he blasted the West for thinking Russia could be defeated on the battlefield. Moscow's opponents "do not conceal their aim to deal our country a strategic defeat", he said.
"I will say directly that these are illusionary calculations, that can be made only by those who do not know Russia's history." Russia has faced fresh accusations of escalating the conflict this week with the United States, South Korea, NATO and Kyiv all saying North Korea had deployed troops to Russia.
Kyiv said Thursday it had intelligence the soldiers had already been deployed to Russia's western Kursk region, where Ukraine is mounting a cross-border offensive. Putin refused to confirm or deny the reports on Thursday, instead accusing Ukraine and the West of aggravating the conflict.
Putin will later sit down for talks with United Nations Secretary General Antonio Guterres in the pair's first meeting since April 2022. The UN chief had pleaded earlier for a "just peace" in Ukraine in a speech delivered in front of Putin.
"We need peace in Ukraine. A just peace in line with the UN Charter, international law and (UN) General Assembly resolution," Guterres told the summit. Ukraine has strongly criticised Guterres's decision to meet the "criminal Putin".
Guterres also demanded an "immediate ceasefire" in Gaza, the release of hostages and an "immediate cessation of hostilities" in Lebanon. Other world leaders at the summit also called for an end to Israel's wars in Lebanon and Gaza, with Palestinian president Mahmud Abbas saying Israel was trying to starve Gazan civilians and drive them from their territory.
Xi warned about "serious challenges" in the world and said he hoped BRICS countries could be a "stabilising force for peace". "We need to continue to push for a ceasefire in Gaza, relaunch the two-state solution and stop the spread of war in Lebanon. There should be no more suffering and destruction in Palestine and Lebanon," Xi said.
Iranian President Masoud Pezeshkian slammed the UN Security Council's role in front of Guterres, saying international bodies "lack the necessary efficiency to extinguish the fire of this crisis".