The Kardashians are on board with Caitlyn Jenner and Lamar Odom teaming up for their new sports podcast -- despite reports suggesting they were blindsided, the fam actually gave it a thumbs-up ... TMZ has learned.

Sources close to Caitlyn tell TMZ ... the Olympian spoke with her former stepdaughter, Khloe Kardashian, after she was approached last year about a possible collab with Koko's ex-husband. We're told Khloe was very supportive of the endeavor, which pays tribute to the family's famous reality show with its title, "Keeping Up With Sports."

Khloe thought it was a great idea for Caitlyn and Lamar to cohost the show together, given they are both champions in their own right. Remember, Cait and LO were always close during the NBA star's marriage to the Good American founder, and afterward, they remained friendly.

We're told Kim Kardashian, as well as CJ's daughters, Kylie and Kendall Jenner, were all made aware of the project, and gave their stamp of approval.

Now, Caitlyn did not loop in Kris about the project, but we're told there hasn't been any tension because of it. Ya gotta figure one of the daughters gave Kris a heads-up ... as they're not a fam that tends to keep secrets -- from each other, anyway.

Not to mention, the first episode with Sugar Ray Leonard probably wouldn't have happened if Kris really had an issue ... since we're told the boxing champ is a close personal friend of hers.