Russian Defence Minister Sergei Shoigu said there were 16,000 volunteers in the Middle East ready to fight alongside Russia-backed forces.
US officials said these could include Syrians skilled in urban combat.
Moscow is a long-standing ally of Syria and Mr Putin has been a key backer of Syrian President Bashar al-Assad in the country’s civil war.
“If you see that there are these people who want of their own accord, not for money, to come to help the people living in Donbas, then we need to give them what they want and help them get to the conflict zone,” Mr Putin told his defence minister.
Mr Shoigu also proposed handing over captured Western anti-tank missile systems to Russian-backed rebel fighters in the breakaway Ukrainian regions of Luhansk and Donetsk in the Donbas region.
“Please do this,” Mr Putin said.
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Ukrainian President Volodymyr Zelensky, responding in a video message, said “thugs from Syria” would be coming to kill people “in a foreign land.”
Foreign fighters, including former and current British army personnel, have also been arriving in Ukraine to fight for the government in Kyiv.
Mr Zelensky said recently that 16,000 foreigners had volunteered for the cause, part of what he called an “international legion”.
Charles Lister, an analyst with the US-based Middle East Institute, questioned how useful any Syrian forces would be to Mr Putin.
“If [President] Assad’s regime begins sending troops to Ukraine, they’ll be no more than cannon fodder in a battle and environment that’s completely alien to them,” he wrote on Twitter.
There was no evidence of any actual recruitment of Syrians having taken place, he added.
In Dnipro, a major stronghold in central eastern Ukraine, one person was reported dead in air strikes
The fighting is driving increasing numbers of people to flee the country, with refugees now totalling 2.5 million
According to the Wall Street Journal, US officials have told the paper that Russia has recently been recruiting fighters from Syria, hoping their expertise in urban warfare can help take Kyiv and deal a devastating blow to the Ukraine government.
At the same time, US private security firms have been seeking to recruit former soldiers to help evacuate people from Ukraine.