Trump friend and Newsmax CEO Chris Ruddy says President Trump is thinking about firing the special counsel in the Russia investigation, Robert Mueller.

"I think he's considering perhaps terminating the special counsel," Ruddy told PBS' host Judy Woodruff on "NewsHour." "I think he's -- he's weighing that option." Ruddy referred to a comment "one of his lawyers said on television recently." And the Newsmax CEO also told Woodruff that he thought firing Mueller would be "a very significant mistake."

The lawyer Ruddy was referring to was Jay Sekulow, a member of the president's legal team, who was asked on Sunday if Mr. Trump would promise not to fire the special counsel.

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"I'm not going to speculate on what he will or will not do," Sekulow said on ABC News' "This Week with George Stephanopoulos." It is, Sekulow said, "an issue that the president with his advisers would discuss if there was a basis."

Late Monday evening, a senior White House official told CBS News that "Chris was speaking for himself and did not speak to the president." Ruddy said Tuesday in an appearance on CNN that he had not spoken with the president before his appearance on "NewsHour," and he called the White House statement about his comments a "bizarre press release." Ruddy also pointed out that the White House did not deny the content of what he had said. He reiterated that "it would be a mistake to fire Mueller," and added, "but I also think the basis of his investigation is flim-flam."

Further, Ruddy told PBS' Judy Woodruff that Mr. Trump met with Mueller a few days before he was appointed special counsel, in order to talk to him about taking another turn as FBI director.

Mr. Trump, Ruddy said, "was looking at him potentially to become the next FBI director. That hasn't been published but it's true."

Mueller has already served 12 years as FBI director -- two years longer than the 10-year term.

Ruddy argued that Mueller should not have taken the job of special counsel because he was under consideration for the other position and had had the private meeting with the president.

Robert Mueller speaks during a farewell ceremony as he retired from the FBI after 12 years as director, August 1, 2013. Getty

CBS News' Katiana Krawchenko and Jillian Hughes contributed to this report.