Barrasso, the chairman of the Senate Republican Conference, made those remarks Tuesday on "Your World," after Rep. Justin Amash, R-Mich., became the first Republican lawmaker to call for the president's impeachment.
"He's one man who has his own personal opinion," Barrasso, R-Wyo., said of Amash.
"I have come to a very different opinion from reviewing the documents," Barrasso told host Neil Cavuto. "No collusion. None. No conspiracy. None. To me, this is over, it's beyond us."
Cavuto noted that many in the GOP "came down like a ton of bricks" on Amash, who was also rebuked by Trump on Twitter.
"If the House of Representatives wants to do what they seem to want to do, which is travel the path to impeachment, let them," Barrasso said. "There's going to be no appetite for that in the United States Senate."
Barrasso said that, while home in Wyoming over the weekend, he heard nothing from his constituents about the the impeachment debate.
Instead, he said Wyoming residents are concerned about maintaining a "strong, healthy economy" and preventing policies that would take them off their employer-sponsored health insurance plans.