LeVar Burton says he’s looking "for the right game show" to host after his interest was piqued – and his hopes dashed – by his recent guest stint on "Jeopardy!" and the social media support he received.

On "The Daily Show With Trevor Noah" last night, Burton expressed gratitude to his longtime fans who have supported him since his "Reading Rainbow" days and were vocal about their desire to see him replace the late Alex Trebek as host of "Jeopardy!" Despite the online support, Burton lost the gig to, at first, Mike Richards, and then to Mayim Bialik and Ken Jennings.

Burton said he first took notice of his fans’ devotion several years ago, with the launch of a Reading Rainbow Kickstarter drive. "I discovered then that the generation of adults now who grew up on "Reading Rainbow," they were down with whatever it is I wanted to do," Burton told Noah, "and the same was true with this ‘Jeopardy!’ thing."

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"I made it public that I wanted it for myself," he continued, "that it made sense to me, and they were all about it. It made as much sense to them as it did to me. They wanted it for me as much as I wanted it."

But the "Star Trek: Next Generation" actor said he’s already moved on from the experience.

"They say be careful of what you wish for because what I found out is that it wasn’t the thing that I wanted after all," he said. "What I wanted was to compete. I mean I wanted the job, but then when I didn’t get it, it was, like, well, okay, what’s next?" He added that he "couldn’t have dreamt" the opportunities – which he didn’t specify – that have come his way since the "Jeopardy!" experience.

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Noah suggested that Burton develop his own game show, which the actor suggested he’s considering. "I never thought about hosting any other game show outside of 'Jeopardy!,' but they went in a different direction with their show, which is their right, and now I’m thinking, well, it does kind of make sense. Let me see what I can do, so we’re trying to figure out what the right game show for LeVar Burton would be."