The trade war between the U.S. and China hasn't had an effect on Google's fast-growing cloud business, according to Google Cloud CEO Thomas Kurian.

In a CNBC interview at the Sibos financial services conference in London Thursday, Kurian said the cloud business is seeing "enormous growth around the world," adding it has "not been affected by the trade war."

Kurian pointed to Google Cloud's "large presence" in Hong Kong and Taiwan and didn't rule out further expansion into China's cloud market.

"We continue to monitor the demand for our technology from Chinese customers," he said.

Cloud services in China are currently dominated by Chinese tech giants like Alibaba and Tencent. Asked whether he sees competition from those local players, Kurian replied, "we worry about everybody."