Multiple outlets also reported that Trump also planned to remove deputy national security advisor Mira Ricardel, who is a top staffer to national security advisor John Bolton.
In an unusually harsh statement Tuesday, the first lady's spokeswoman said Ricardel "no longer deserves the honor of serving in this White House."
The Wall Street Journal, citing a White House official, reported shortly after that statement that Ricardel had been fired and escorted from the White House. But another official told reporters the story was untrue, and that Ricardel still worked at the White House.
Asked to confirm or deny that Ricardel still worked at the White House, Grisham told CNBC: "I have no idea."
Multiple outlets had reported Tuesday that Ricardel had clashed with the first lady's staff during a trip to Africa last month, among other disputes. But Grisham had told CNBC shortly before noon ET that Ricardel was "still there to my knowledge" and appeared to deny the report that there had been a dispute.
Earlier Tuesday afternoon, Ricardel had attended a White House event, where President Donald Trump led a ceremony for the religious holiday Diwali.
NBC's report followed a slew of news that Homeland Security Secretary Kirstjen Nielsen may be on her way out, too.
The secretary's potential forthcoming departure was reported a week after the midterm elections and days after the forced resignation of Attorney General Jeff Sessions.
But multiple outlets reported recently that Trump was planning a staff shakeup that would lead to both Nielsen and Kelly being removed.
"The Secretary is honored to lead the men and women of DHS and is committed to implementing the President's security-focused agenda to protect Americans from all threats and will continue to do so," DHS press secretary Tyler Houlton said in a statement Tuesday.
Nielsen had served in the Trump administration under Kelly before being confirmed to the Cabinet-level position in December.
Trump had praised Nielsen over the summer after she defended the administration's border security goals amid a roiling controversy surrounding then-Attorney General Jeff Sessions' "zero tolerance" immigration policy.
But in the White House tell-all book "Fear," Watergate reporter Bob Woodward wrote that Kelly had fought to convince Trump to confirm Nielsen.
"She's terrible," Trump reportedly told Kelly. "You're the only one that thinks she's any good. Maybe we'll have to withdraw her nomination." Trump ended up supporting Nielsen.
On Wednesday, Trump announced that Sessions, who said he was resigning at the president's "request" in a letter to Trump, would be replaced with Acting Attorney General Matthew Whitaker before a permanent replacement was selected.
That announcement, which came less than a day after Democrats won back majority control of the House in the midterm elections, was immediately met with criticism from Democrats and legal experts, who alleged that Whitaker was unconstitutionally appointed and was selected because of his past skepticism toward special counsel Robert Mueller's Russia probe.
contributed to this report.
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