'Jeopardy!' Wanted Mayim Bialik as Daily Host, Found Way to Hire Her Anyway

Mayim Bialik's upcoming role as one of the new hosts of "Jeopardy!" might have been even greater if she just had the time ... TMZ has learned

According to our Sony Studios sources ... "The Big Bang Theory" star became a frontrunner with bosses at Sony to permanently host the game show after guest hosting in March. On top of that, we're told the crew loved working with her AND she also tested highest in focus groups.

Our sources say several Sony execs were "very interested" in Mayim for hosting duties on the daily syndicated program, but because of her other commitments -- she stars and executive produces "Call Me Kat" on FOX, and hosts a podcast -- they knew it wasn't going to be possible.

So, because they loved her so much ... we're told "Jeopardy!" honchos came up with the idea for 2 hosts -- one for the daily show, and Mayim for the quiz show's primetime and spin-off specials.

We're told this became a top priority, and after about 6 weeks of negotiations ... Mayim reached a multi-year, multi-million-dollar deal to do just that, including the upcoming "Jeopardy! National College Championship" ... which will air in primetime on ABC.

As we reported ... EP Mike Richards was named the new host of the syndicated "Jeopardy!" while Mayim will do her thing on a more part-time basis.