Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R-Ariz.) on Sunday said President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE could see a Republican or independent challenger in 2020, adding that he’s not ruling out a possible White House bid himself.

“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,” Flake said on ABC’s “This Week.”

Flake, who announced he is not running for reelection to the Senate in 2018, has been a vocal critic of Trump and the Republican Party under his leadership.

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Flake said Sunday the GOP is largely appealing to "older white men," adding that the party must find a governing philosophy to be successful in the future.

"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 [Sens.] Bernie Sanders Bernie SandersThe Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power Bernie Sanders: 'This is an election between Donald Trump and democracy' The Hill's 12:30 Report: Trump stokes fears over November election outcome MORE [I-Vt.] or Elizabeth Warren Elizabeth WarrenHillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline Democratic senators ask inspector general to investigate IRS use of location tracking service MORE [D-Mass.] on the far left of the Democratic Party," Flake said.

"That leaves a huge swath of voters in the middle," he added.

Flake said Trump is “certainly” inviting a challenge from an independent candidate, and is “probably inviting a Republican challenge as well.”

Asked if he’s open to running for president in 2020, Flake said, “I don’t rule anything out, but it’s not in my plans.”