On Monday night, Chris Ruddy, a friend of President Trump's, told "PBS NewsHour" host Judy Woodruff that the president was "considering perhaps terminating the special counsel" appointed to oversee the Russian Federation investigation, Robert Mueller.
Some of Mr Trump's allies have begun questioning Mr Mueller's credibility as the investigation intensifies.
But it is a line of thinking that is making its way to the president's ears. In response to a question about a hypothetical presidential order, he says he's "not going to follow any orders" he doesn't believe to be "lawful and appropriate".
"It's a mistake to pretend that this is going to be some neutral investigation", Gingrich said.
"I think the President should get on the work that is so important that he do and at this point let this investigation run its course". "(Attorney General) Jeff Sessions is recused here, so it would be up to (Deputy Attorney General) Rod Rosenstein, who was the person who just appointed Bob Mueller a couple of weeks ago".
Now, however, some Republicans are suggesting that Mueller ought to be dismissed, pointing to Mueller's selection of key investigators who made campaign donations to Trump's Democratic challenger, former U.S. Secretary of State Hillary Clinton.
"Special counsel Mueller may be fired only for good cause", Rosenstein said. Trump, who isn't typically shy about leveling criticism, especially on Twitter, hasn't commented on the longtime former Federal Bureau of Investigation director.More news: Britain should stress jobs, prosperity in Brexit talks: Hammond
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"No, I have not", he said.
In an earlier hearing Tuesday before a Senate appropriations subcommittee, Rosenstein said Mueller will have the "full independence he needs to conduct that investigation", and that he has not spoken to Mueller about the substance of the investigation since appointing him.
The member of Trump's legal team Jay Sekulow, who spoke on the program "This Week" on ABC on Sunday, explained that Trump was considering such an idea. But the president is going to seek the advice of his counsel and inside the government as well as outside. "I will defend the integrity of that investigation", Rosenstein said.
White House officials would not confirm Ruddy's assertions, saying "Chris speaks for himself".
In 1973, former President Richard Nixon asked then-Attorney General Elliot Richardson and Deputy Attorney General William Ruckelshaus to fire Watergate special prosecutor Archibald Cox.
Peter Carr, a spokesman for Mueller, declined to comment on the issues Gingrich and others have raised.