Sen. Ted Cruz suggested Wednesday that Republican primary voters should be the ones moderating GOP debates, rather than liberal TV hosts who were roundly criticized during Wednesday night's Republican debate on CNBC.

"Why is it that we keep having debates where the moderators … no one in their right minds thinks any of the moderators actually will vote in a Republican primary?" Cruz asked on Sean Hannity's show on Fox. "In my view, Republican primary debates ought to be moderated by people who would vote in a primary."

Cruz tossed out Hannity's name as one possibility, along with conservative talk radio show hosts Mark Levin and Rush Limbaugh.

Hannity replied, "I'm in," adding that he could speak for the other two men that they would be in as well.

"I'd ask Reince Priebus," Hannity said of the Republican National Committee chairman, who himself voiced his displeasure with the CNBC moderators shortly after the debate.

Republican primary voters "would love to hear that debate," Cruz told him.

"It wouldn't be a 'gotcha' debate," Hannity said, to which Cruz responded, "Exactly."

In the Wednesday night's debate, Cruz took the CNBC moderates to task, saying the questions they asked "illustrate why the American people don't trust the media." His monologue was greeted by much applause by the audience.

He continued his harsh critique of the mainstream media on Hannity's show.

"We've seen now over and over again where the media … they are the Democrats' cheerleaders, and in these debates … every question is an insult, every question is asking one Republican to attack another Republican," he said.