The U.S. relationship with China is "probably as poor as" it was before the Nixon administration opened up ties more than four decades ago, former Fed governor Kevin Warsh told CNBC on Thursday.

"We're at the risk of a real cold war" between the world's two biggest economic superpowers, said Warsh, who had been on President Donald Trump's short list for Fed chairman before Jerome Powell was chosen. "The last 30 years we've been living and breathing globalization as if it's an inevitable force."

Warsh was using the term "cold war" to mean an economic standoff, not the decades-long "mutually assured destruction" nuclear stalemate between the U.S. and Russia that began to thaw in the detente period that led to the fall of the Berlin Wall in 1989.

"We are probably on the precipice of a brand new relationship with the Chinese," Warsh said in a "Squawk Box" interview. "Could we be at the beginning of a 10- or 20-year cold war? That has huge implications for the economy."

Warsh, a distinguished visiting fellow at the Hoover Institution think tank, said ties between the nations are deteriorating at the government-to-government and business-to-business levels.

"Five or 10 years from now we might see two poles: a Chinese-centric world and an American-centric world. And the [other global] economies and countries will have to plug into one or both," he said.

China has certainly been moving toward a more consumer-led economy and away from state-funded stimulus for growth. But China's brand of capitalism still has an aspect of being state-directed as its core, which is quite different from the free-market capitalism of the U.S.

Warsh said the new U.S.-China dynamic is bigger than Trump. "I think whoever is sitting in that seat will have a new relationship with China."

"Great power relationships are not about how many soybeans you're going to buy [or how] many Boeing airplanes you're going to buy. It's about your core interests," he added, suggesting the current trade war is only one part of the ideological differences between communist China and the democratic United States.

"I suspect that there will need to be between [Chinese President Xi Jinping] and President Trump a great summit, among great powers. And that requires two countries that want to have that discussion," said Warsh, who was Fed governor from 2006 to 2011 during the bursting of the housing bubble and the 2008 financial crisis.

Before his appointment to the central bank, Warsh worked as an economic advisor in the George W. Bush administration and in the mergers and acquisitions department at Morgan Stanley.