U.S. Defense Secretary Jim Mattis briefs members of the media on Syria at the Pentagon in Washington, United States on April 13, 2018.

The White House is actively discussing possible replacements for Defense Secretary James Mattis, according to a report published in The Washington Post on Wednesday.

The newspaper reported that discussions about who would succeed the top Trump administration official predated reports this week that Mattis had insulted the president's intelligence. One senior administration official told the paper, however, that "speculation about who replaces Mattis is now more real than ever."

On Tuesday, The Washington Post published excerpts from "Fear," a forthcoming book written by Bob Woodward. Mattis told associates that the president had the understanding of "a fifth- or sixth-grader," Woodward wrote.

Wednesday's report was written by Josh Rogin, a national security columnist for the newspaper. The Department of Defense did not immediately respond to a request for comment from CNBC. Mattis has called the claims in Woodward's book "fiction."