Story highlights Republican Sen. Jeff Flake has broken from Trump in the past

Trump is trying to find someone to run against him in his Senate primary

Washington (CNN) Republican Sen. Jeff Flake insists that he wants to "work with" President Donald Trump -- despite Trump's attempts to find a challenger to replace the sitting senator in his upcoming election.

The frequent Trump critic refrained from adding fuel to the fire Thursday morning on Fox News after Trump's rally in Arizona on Tuesday -- at which the President, without using his name, slammed Flake as "weak" in front of his home-state crowd.

When asked why Trump is not his biggest fan, Flake told Fox News, "I don't know. I want to work with the President when I think that he's right, and I'll challenge him when I think that he's wrong."

After Tuesday's rally, Trump tweeted a day later: "Phoenix crowd last night was amazing -- a packed house. I love the Great State of Arizona. Not a fan of Jeff Flake, weak on crime & border!"

Phoenix crowd last night was amazing - a packed house. I love the Great State of Arizona. Not a fan of Jeff Flake, weak on crime & border! — Donald J. Trump (@realDonaldTrump) August 23, 2017

Before taking the stage in Phoenix, Trump huddled privately with potential Republican primary challengers to Flake.

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