Kelly, amid a number of reports of White House chaos and staff shake ups, reportedly tells the president "no" too often for Trump's liking.
General McMaster, whose job requires him to negotiate internal disputes among factions within the administration, as well as deal directly with foreign officials, is operating with the public expectation that every day may be his last.
McMaster, Trump's chief national security aide and leader of the National Security Council, has been in the post for just over a year.
The rumors follow Secretary of State Rex Tillerson's firing via Twitter on Tuesday, leaving many White House staff wondering who is next on Trump's hit list.
But the lack of any resolution to the reports of coming firings is leaving numerous president's top advisers in a kind of political limbo that threatens to undermine their effectiveness until their fates are revealed, one way or the other. The president recently told an ally that he was still frustrated by an interview that Kelly gave to Fox News almost two months ago in which he suggested that Trump had "evolved" in his thinking about the need for a wall on the Mexican border. She said Trump had indicated that no changes were coming. The descriptions of the administration in turmoil are based on interviews with 19 presidential advisers and administration officials, many of whom spoke on the condition of anonymity to offer candid perspectives. "He asked me to pass that message along to Gen. McMaster".
Yet that candor, and McMaster's occasional slow-walking of Trump orders that the national security team thought ill-advised, made for some tense moments that provoked Trump to explode at McMaster. Kelly has also worn on the president, confidants of the president said.
McMaster is not the only senior official on thin ice with the president.
According to the newspaper, Veterans Affairs Secretary David Shulkin, Housing and Urban Development Secretary Ben Carson, Environmental Protection Agency Administrator Scott Pruitt and Interior Secretary Ryan Zinke have reasons to be anxious about their jobs. "I know the two of them have been in meetings today".
Trump enjoys watching his subordinates compete for his approval, the officials said.
Kelly and Trump are known to clash at times, but the president has repeatedly expressed confidence in his chief of staff, telling a gathering of Marines in San Diego this week that Kelly is "doing a great job". It's supposed to be about stability and continuity.
Information for this article was contributed by Ashley Parker, Josh Dawsey, Philip Rucker, Carol D. Leonnig and Greg Jaffe of The Washington Post; by Michael D. Shear and Maggie Haberman of The New York Times; by Brian Bennett of the Los Angeles Times; and by Margaret Talev of Bloomberg News.