As the U.S. mulls its next move against North Korea, some have suggested that sanctioning the major Chinese banks could be the most effective way to pressure the rogue nation into halting its nuclear program.

Targeting the big lenders from the world's second-largest economy is not a new idea. And it would not necessarily just be a way to lash out at Beijing for not controlling Pyongyang sufficiently: Some Chinese banks, like the Bank of China, are said to have helped North Korea evade sanctions.

But the big Chinese banks have so far avoided any punishments by the U.S., which has instead blacklisted smaller players such as Bank of Dandong for financing North Korea. That could change after the hermit nation claimed over the weekend that it successfully tested a hydrogen bomb — a much more powerful weapon compared to those it previously tested.

In response, President Donald Trump tweeted that the U.S. is considering "stopping all trade with any country doing business with North Korea" and Treasury Secretary Steve Mnuchin is reportedly drafting a harsher sanctions package.

Donald Trump tweet: The United States is considering, in addition to other options, stopping all trade with any country doing business with North Korea.

China is North Korea's largest trading partner, accounting for 85 percent of the latter's trade and has a "fair amount of leverage" over the hermit nation, Bejoy Das Gupta, Asia Pacific chief economist at the Institute of International Finance told CNBC's "Squawk Box."

In an August announcement by the Treasury Department, more Chinese entities were added to the U.S. sanctions list. Mnuchin at the time said the Treasury "will continue to increase pressure on North Korea" by, among others, "isolating them from the American financial system."

All big four state-owned banks in China have in recent years increased their presence in the U.S., where their operations now include providing loans, issuing bonds and financing trade activities.