WASHINGTON (BLOOMBERG, REUTERS) - US President Donald Trump said his administration is "doing very well" on making a trade deal with China ahead of a fast-approaching deadline, and did not rule out another government shutdown or other action to get funding for a US-Mexico border wall.

"I don't take anything off the table. I don't like to take things off the table," Mr Trump said in an interview on CBS's "Face the Nation" that will air on Sunday (Feb 3).

The wide-ranging interview was conducted on Friday. Mr Trump's comments came days before the annual State of the Union address to Congress, set for Tuesday night.

Mr Trump also said he does not think Secretary of State Michael Pompeo plans to leave his administration to run for the Senate from Kansas, as has been rumoured recently.

"He tells me he wouldn't want to leave," he said. "I asked him the question the other day, he says he's absolutely not leaving. I don't think he'd do that."

The president said the date of his next summit with North Korea's Kim Jong Un would be announced shortly. "I think North Korea wants to make a deal," he said.

Trump also said it was important to keep a US military base in Iraq so that Washington can keep a close eye on Iran, according to the interview.

"One of the reasons I want to keep it is because I want to be looking a little bit at Iran because Iran is a real problem," he said in excerpts. "I want to be able to watch Iran," adding that he is willing to leave a smaller number of troops and "intelligence" in Afghanistan.

Sending military to Venezuela is "an option," Trump said, but he has turned down President Nicolas Maduro's request for a meeting.