Former House Speaker Newt Gingrich, who led the Republicans' impeachment effort against President Bill Clinton in the 1990s, said Monday that President Donald Trump shouldn't worry about the House committees' impeachment inquiry.

When asked on "CBS This Morning" what he would advise the president to do, Gingrich replied, "Relax. Rely on the Senate.

"He will not be convicted, period," Gingrich said. "It's inconceivable."

He also called it an "elaborate farce" that the House is keeping secret the identity of the whistleblower who revealed the president's phone call asking "a favor" of Ukraine's President Volodymyr Zelensky. Gingrich warned that if the House impeaches Mr. Trump and the trial to remove him is held in the Senate, "Guess what the first thing Lindsey Graham is going to do? He's going to unmask who the whistleblower is."

Co-host Tony Dokoupil said, "The polls show that Americans do support the impeachment inquiry, and you advised the president not to talk about it, but he is."

Former House Speaker Newt Gingrich. CBS News

Gingrich replied, "My view is if you keep getting a one-sided barrage of information, this is a president who on average has had 92% negative coverage, and he's still standing, by the way, has a larger following than all three networks combined."

"What's your point about that?" asked co-host Gayle King.

"His ability to communicate is astounding. The base you see at these rallies is not trivial," Gingrich said.

In 1998 Gingrich told the Los Angeles Times that the fastest way for President Clinton to get through impeachment was to instruct his staff to cooperate totally. "That's not this White House's strategy," said co-host Anthony Mason. "Would you argue they're making a mistake?"

"The two things are radically different," Gingrich said. He took issue with House investigators hearing testimony in secret, and called the House Judiciary, Intelligence and Oversight Committees' impeachment inquiry "a total kangaroo trial, and a violation of everything in terms of the American system."

Trump, the Doral resort and the G-7

Dokoupil asked, "The White House seems to be confusing even some of its own allies and supporters on Ukraine aid, Syria, on this whole Doral/G-7 thing. What's going on over there?"

"Well, I think that the president frankly makes too many decisions on his own, and doesn't draw in people to get their advice," Gingrich said. "And it's part of what [was] his strength at one time. I mean, nobody would have advised him to run; nobody would have advised him he could win the nomination; nobody would have advised him on Election Day he could beat Hillary [Clinton]."

"If you were chief of staff right now, what would you advise?" Dokoupil asked.

"I would advise to go slightly slower and listen more carefully," he replied. "They could have avoided the whole Doral thing by simply checking with five or ten people. And the reaction would have been so negative the president would have said, 'OK, that's not doable.'"

Mason said, "But there are reports that he was told that he probably shouldn't do that, and he did it anyway."

"Well, … " Gingrich replied.

King asked, "Are you surprised that when he finally announces over the weekend that he's pulling out [of the Doral decision], he blames, you know, 'crazed Democrats,' 'fake media,' 'fake news anger,' as opposed to saying 'I was wrong, I made a mistake, let's move on'?"

"Never apologizes," Gingrich said.

"Does that ever get to you?"

"No. It's a technique he learned dealing with Page Six in the 1980s: he is always on offense. And if you hit him, he immediately counter-attacks. This is Trump. People keep being shocked every week to discover that Trump is Trump."

Gingrich's latest book, "Trump vs. China: Facing America's Greatest Threat" (Center Street), is about the challenges the U.S. faces from Beijing. In it he writes, "If the U.S. doesn't wake up and realize that China is not a friendly neighbor, it may be too late."

Gingrich said Chinese President Xi Jinping "approaches everything, every day, from the standpoint of maximizing the power of the Chinese Communist Party, maximizing China's place in the world, and frankly, they're doing very well."

"We are in real danger of our grandchildren learning Chinese," Gingrich said.