This morning President Donald Trump said he thinks Volodymyr Zelenskyy is ready to give up Crimea.
According to foreign media, this would signal a major U-turn by the Ukrainian president, who has repeatedly ruled out handing over territory to Russia and saying the move would be against Kiev's Constitution.
The peninsula was illegally annexed by Russia in 2014 and Moscow's foreign minister has insisted that Russia will not negotiate "its own territory".
So what makes Crimea so important to both sides?
In 2013-14, a popular uprising swept Ukraine for several weeks, ultimately forcing Viktor Yanukovych, the pro-Moscow president of Kiev, from office.
While Ukraine was in turmoil, Vladimir Putin seized the opportunity to send troops to invade Crimea, a diamond-shaped peninsula in the Black Sea.
Those troops arrived in Crimea in plain uniforms and Putin quickly called a vote on unification with Russia, which Ukraine and the West condemned as illegal.
Moscow's illegal annexation on March 18, 2014, was recognized internationally only by countries such as North Korea and Sudan.
In Russia, it sparked a wave of patriotism and "Krym nash" - the phrase "Crimea is ours" - became a rallying cry.
Putin has called Crimea "a sacred place" and has prosecuted those who publicly argue that it is part of Ukraine.
Why is it important?
Russia has spent centuries fighting for Crimea.
But Soviet leader Nikita Khrushchev transferred Crimea from Russia to Ukraine in 1954, when both were part of the Soviet Union.
In 1991, when the Soviet Union collapsed, the peninsula became part of independent Ukraine, writes A2 CNN.
By the time Russia invaded, Crimea had been part of Ukraine for 60 years and had become part of the country's identity.
Zelenskyy has vowed that Russia "will not be able to steal" the peninsula, writes A2 CNN.
For each side, possession of Crimea is key to controlling activities in the Black Sea, which is a critical corridor for the world's grain and other goods. (A2 Televizion)
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