Cornyn responded, "I read that the president’s own lawyer says that’s not going to happen. I think that would be a mistake, myself."
"There are plenty of FBI agents and prosecutors who have not been politically involved on behalf of Democrats or overtly critical who can serve in this important investigation," Cornyn said. "I have confidence in Director Mueller, I just think that he would be concerned about the appearance of conflicts of interest that would undermine the integrity of the investigation."
Cornyn also said he's "confident" the Republican tax plan will pass this week, saying it will benefit the economy and individual Americans.
"We're going to get the economy roaring back again, and improve pay, and increase jobs, and make America more competitive in the global economy, as well as simplifying the tax code and giving everybody in every tax bracket a tax cut," Cornyn said. "I am confident we will pass this, probably on Tuesday."
Stephanopoulos asked if Republicans would still be able pass the tax legislation if Sen. John McCain of Arizona, who is currently in a hospital as he battles cancer, does not return to Capitol Hill by Tuesday.
“Well, I won't speculate on Senator McCain's health. We hope he comes back,” Cornyn said.
Stephanopoulos also asked Cornyn why a provision was added to the bill at the last minute that could give a tax break to people who earn income from real estate through limited liability corporations, LLCs, and which could potentially benefit the president and other Republican elected officials who invest in real estate.
"We were working very hard. It was a very intense process," Cornyn said. "What we tried to do was cobble together the votes we needed to get this bill passed, at the same time maintaining the largest tax cuts we’re going to be seeing since 1986."
"So is that how you go Sen. Corker [to support the bill], with this provision?" Stephanopoulos pressed, referring to Sen. Bob Corker, R-Tenn., who voted against the Senate version of the tax bill, but now says he will support the final bill this week.
"Well, the particular provision you're talking about, honestly, is just one piece of a 1,000-page bill which is going to grow the American economy," the Texas senator responded.
Cornyn also discussed Republican Roy Moore's loss in the Alabama Senate race last week.
Stephanopoulos noted that Cornyn was "not a fan of Roy Moore" in the election. "Do you think the GOP dodged a bullet with that loss?" he asked.
"Well, I think the explanation for Alabama was we had a flawed candidate who won the Republican primary and who couldn't win the general election. That's really not a new lesson. That's an old lesson remembered or demonstrated once again," Cornyn said. "My party needs to do is make sure we nominate electable candidates, good candidates who can win general elections."
Asked about former White House senior adviser Steve Bannon, who backed Moore in Alabama, and his role in 2018, Cornyn responded, “Mr. Bannon can do whatever he sees fit. It's a free country.”
“But I don't think his track record, particularly now in losing Alabama, one of the reddest states in the country, particularly commends him for his expertise,” Cornyn added.