President Donald Trump makes an appearance via monitors during Sarah Huckabee Sanders daily press briefing on Jan. 4th, 2018.

The suggestion by the White House press secretary came a day after Bannon's scathing comments about the president's family were published ahead of the release of "Fire and Fury," a tell-all book about the Trump White House by author Michael Wolff.

As of Thursday afternoon, Bannon was still employed by Breitbart, and spokespeople for the company did not immediately respond to a request for comment about Sanders' remarks.

"I certainly think that it's something they should look at and consider," Sanders said, when asked if the generally pro-Trump news outlet should consider firing Bannon, its longtime chief executive.

White House press secretary Sarah Huckabee Sanders said Thursday that Breitbart News should consider parting ways with executive chairman Steve Bannon, the former chief strategist to President Donald Trump .

According to Wolff's reporting, Bannon said that a meeting between Trump's eldest son, Donald Trump Jr., and a Russian lawyer in 2016 was "treasonous" and "unpatriotic."

Sanders called the book "trash," "fraudulent" and "tabloid gossip" and labeled Bannon an employee who "got fired" and Wolff "an author who no one has ever heard of before today."

Sanders' vitriol followed brief comments from Trump on Thursday morning, in which the president sounded pleased that Bannon had paid him a compliment on his Breitbart Radio show the night before.

"He called me a great man last night, so, you know, he obviously changed his tune pretty quick," the president told reporters Thursday at the White House.

"I don't talk to him," Trump added.

Sanders also attempted, without success, to convince reporters that Trump and his onetime chief strategist were merely work colleagues. "I'm not aware that they were ever particularly close," she said.

The president's remarks were a surprising departure from the statement he released Wednesday in response to Bannon's comments. Trump unleashed on his former key advisor, saying Bannon had "lost his mind."

In his statement, the president said Bannon — the nationalist firebrand — "had very little to do" with his electoral victory in 2016. "Steve is learning that winning isn't as easy as I make it look," Trump said.

Bannon called Trump "a great man" on the Wednesday radio show, adding, "You know I support him day in and day out."

A Trump lawyer has sent a cease-and-desist letter to Bannon demanding that he stop making "disparaging" comments about the president and his family.