Thune, meanwhile, said he hasn't made a decision to challenge President Barack Obama but noted "the clock is ticking."
"I think these are interesting times and you always want to look at where you can best serve your country best," Thune told ABC News. "Obviously, there's a big opportunity on the national field."
Thune, elected to a second term in November, is among about a dozen would-be Republicans pursuing the party's nomination. Some are already visiting early nominating states of Iowa, New Hampshire and South Carolina. None has announced a White House run.
"It won't be long," Thune said of his timeline for making a decision. "We realize that if you're going to do this, you have to get moving."
McConnell said he hopes the South Dakota lawmaker will make a run in 2012.
"I think John is an extraordinarily impressive individual," he told MSNBC. "I hope he will run. I think he would make a great president of the United States."
When asked if he was endorsing, McConnell laughed.
"I wouldn't want to give him that handicap," McConnell said.