Putin also warned the West on Thursday that it was an "illusion" to think Moscow could be defeated on the battlefield and that any peace deal would have to recognise Russia's control of large areas of Ukrainian territory.
Putin faced calls at the summit from some of Russia's most important allies for the fighting in Ukraine to end.
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."Some analysts believe next month's US presidential election could be critical to future ties and the conflict in Ukraine.
'Realities on the ground'
Leaders or representatives of 36 countries attended the three-day BRICS summit, including Chinese President Xi Jinping and Indian Prime Minister Narendra Modi, highlighting the failure of US-led efforts to isolate Russia over its actions in Ukraine.
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."Putin has previously demanded Kyiv effectively capitulate by pulling its troops back as a precondition to ceasefire talks.
Call for end to wars in Middle East
The meeting saw the first visit to Russia from UN Secretary-General Antonio Guterres in more than two years, which drew an angry reaction from the Ukrainian government.
Guterres called for "a just peace" in Ukraine, in line with the UN Charter, international law and General Assembly resolutions. He also urged an immediate end to the fighting in Gaza, Lebanon and Sudan.
"It was the third year of the war, and the UN Secretary-General was shaking hands with a murderer."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 civilians in Gaza and force them to flee the territory.
Chinese President Xi Jinping warned about "serious challenges" in the world and 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."Iranian President Masoud Pezeshkian condemned the UN Security Council's role in front of Guterres, saying international bodies "lack the necessary efficiency to extinguish the fire of this crisis".
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