Russian President Vladimir Putin has been privately signaling that he is open to a cease-fire in Ukraine, the New York Times reported Saturday, despite publicly saying he won't back down from the conflict that has been ongoing since early last year.

More than 10,000 civilians have been killed and more than 18,500 injured since the war began, according to the United Nations, in addition to tens of thousands of troops.

Putin has been indicating since at least September that he is open to stopping the fighting at the current boundary lines, the Times reported, citing two former senior Russian officials close to the Kremlin and other American and international officials.

That's far from Putin's apparent goal of overtaking Ukraine. Russia invaded neighboring Ukraine on Feb. 24, 2022 and quickly overtook large swaths of the country. But Ukrainian forces pushed back hard and successfully forced Russia to retreat from its northern regions. Since Oct. 2022, the battle lines have remained largely the same, with Russia holding parts of the southern and eastern regions of Ukraine.

Putin also "sent out feelers" for a cease-fire last fall, according to the Times, and communicated that he was satisfied with the territory they had taken. But sources cited by the Times also warned that it could be an attempt at "misdirection" or that Putin could change his mind if his troops regain momentum. It's also not clear Ukrainian President Volodymyr Zelenskyy would accept the deal, as Russia still holds parts of the country.

The Russian military had been worn down by early 2023, as professional soldiers were replaced with draftees and prisoners who did not stand up well to Ukraine's forces. Only a small portion of Russians support the war effort, and Putin faced an embarrassing mutiny from mercenary leader Yevgeny Prigozhin.

However, Ukraine has been unable to retake its lost territories. It's facing wavering support in the West and is competing for international attention with the war in Gaza.

Zelenskyy has been lobbying United States leaders to finalize additional aid for his country, including visiting Washington last week to meet with Congressional leaders and President Joe Biden.

Biden has requested $60 billion for Ukraine, as well as $14 billion for Israel, $10 billion for humanitarian assistance and $14 billion for the U.S. border. The package has stalled in Congress as the Republican caucus remains fractured over whether to continue to support Ukraine's fight against Russia.

The Biden administration has warned that it will soon run out of funding for Ukraine's war effort without additional funds approved by Congress. Republicans refused to vote on the supplemental funding request without significant changes to asylum and border policies.

Bipartisan negotiations in the Senate, including White House officials and Homeland Security Secretary Alejandro Mayorkas, have been ongoing for weeks. The Senate hopes to reach a deal and vote on it when Congress returns early next year.