There's only one person in the world now who can influence Putin, says Stephen Roach

The "best thing" that China could do right now is to broker a peace deal between Russia and Ukraine, said economist Stephen Roach.

"There's only one person in the world, I think, who has leverage over Vladimir Putin — and that's [Chinese President] Xi Jinping," Roach told CNBC's "Squawk Box Asia."

"I mean, China's really holding the trump card here and I think it's up to Xi to seize this moment," he added.

Fighting has intensified across many cities in Ukraine and Putin has showed no signs of letting up.

The U.S., U.K. and European Union have scrambled to hit Russia with sanctions after it invaded Ukraine. China, however, has said it won't participate in sanctions and refused to call Russia's attack on Ukraine an invasion. 

China has also abstained from voting on a United Nations resolution to reprimand Russia for invading Ukraine.

Beijing has instead promoted negotiations and positioned itself further away from Russia than was portrayed in early February during a high-profile meeting between Xi and Putin. During that meeting on the opening day of the Winter Olympics in Beijing, the leaders announced a "no limits" partnership, promising to collaborate more against the West.

Roach said China should instead "threaten to pull the rug out" if Putin "doesn't play ball." He said it would be a mistake for Beijing to double down on its partnership with Moscow when the world is putting extraordinary pressure on Russia. Roach said doing so would brand China as guilty by association for a "long, long time."

"He cannot afford to stay that course — that would be a blunder of historic proportions for Xi Jinping," Roach said.