That meeting is sure to be closely watched in the United States, where Trump has come under sustained criticism over his campaign's ties to Russia and his praise of Putin.
US intelligence agencies believe that Putin approved of a wide-ranging campaign to tilt the 2016 election in Trump's favor, prompting US sanctions imposed by former president Barack Obama.
"We'll see where we go from here."
No details were given about the possible safe zones, which have long been discussed, but faltered as Bashar al-Assad's regime and assorted groups of rebels, Kurds, Iranian-backed militias, Al-Qaeda and Islamic State fighters have kept-up a bloody war that has killed an estimated half million people.
The State Department earlier announced that it would send a junior minister to Russian-backed peace talks in Astana later this week.