Flake, who has announced he is not running for reelection when his term expires in 2018, told ABC News' Chief White House Correspondent Jonathan Karl on This Week Sunday that Trump and the Republican party must find a governing philosophy to be successful in the future.
"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," he said.
Flake went on to say that the current Republican platform is mostly appealing to "older white men" and may be countered by a "far left" candidate.
"I do worry, that in the future we'll be faced with a President Trump running for reelection on one side, drilling down hard on a diminishing base, and on the other side you might have, you know, somebody like Bernie Sanders or Elizabeth Warren on the far left of the Democratic Party," he said.
He said the disparity between the likely Republican and Democratic candidates "leaves a huge swath of voters in the middle" and could create an avenue for a third candidate.
"I think he's inviting that," Flake said of Trump. "He's probably inviting a Republican challenge as well ... but certainly an independent challenge."
Flake, who has often been critical of Trump and his administration, said he believes a conservative challenge is important.
"People need to see what a traditional conservative looks like ... [and] what it means to believe in the basic tenets of Republicanism," he said.
Flake said it was unlikely he would oppose Trump himself in 2020, but ultimately left the possibility open.
"I don't rule anything out," he said of a potential presidential bid. "But it's not in my plans."