The U.S.-China trade war is likely to follow President Donald Trump into the 2020 presidential election, Steve Bannon told CNBC on Thursday.

The two countries may be able to agree on smaller issues, but an overall deal is "going to take a while," the hardline former chief White House strategist said in a "Squawk Box" interview. "I don't think that's going to be done by 2020."

However, Bannon has suggested that such a delay might help Trump's reelection campaign because the president could position himself as the only one able to solve the China problem. Last month, Bannon told CNBC, "This is history in real time. This is the most significant thing that any president can possibly do."

Washington and Beijing have been locked in a trade war for nearly a year, with the two sides stepping up tariffs on one another in the past month and threatening additional punitive measures. Trade talks have stalled, though Trump and Chinese President Xi Jinping are set to meet this weekend at the G-20 summit in Japan.

Bannon said he does not believe a deal can be reached in the next year, let alone this weekend. "We're engaged in this," he added. "I don't see any short-term let up on this."

Trump's former pick for the Federal Reserve echoed similar sentiments on Wednesday.

"This trade dispute isn't going to be solved in the next year or two. This is going to be the epic battle of our times," said Stephen Moore, who withdrew his name from Fed consideration in May. "It's going to go on for 10 or 15 years."