"I do believe if the president is running for reelection, if he continues on the path that he’s on, that that’s going to leave a huge swath of voters looking for something else, who are unwilling to go where the president’s going unless he changes course," Flake told ABC News’ Chief White House Correspondent Jonathan Karl on "This Week" Sunday.
"So you’re saying if he is the Republican nominee again, we’re likely to see an independent candidate?" Karl asked.
Flake responded, "Oh yes, I think he’s inviting that. He’s probably inviting a Republican challenge as well ... but certainly an independent challenge."
The Arizona senator, who has announced he is not running for reelection when his term expires in 2018, added that he believes "it is important" for the president to face such a challenge from a conservative.
"I think it is important," Flake said. "People need to see what a traditional conservative looks like ... [and] what it means to believe in the basic tenets of Republicanism", including limited government, economic freedom and free trade.
The Arizona Republican said his opposition to some of the president’s actions would have made a re-election bid tough.