The Kardashians denied The Game did not sleep with the three of them, maybe one

The Kardashians say The Game's lying when he boasted he slept with 3 of them on his track, "Sauce" ... he's wrong about at least 2.

Sources close to the Kardashians tell us you can count out Kylie, Kendall, Khloe, Kourtneyand Kris ... none of them had sex with Game.

The sources acknowledge Kim dated Game back in the day ... so that one's on the table for discussion, but that's it.

Khloe and Game have been pals for years, but the Kardashian sources are adamant ... strictly platonic.

That said, there's an interesting nugget. Game reached out to Kanye to get his blessing for the song, and Kanye said he didn't have a dog in the fight. Interesting ... Game didn't call Kim.

But ... we know Game sticks by his story. He nailed 3 of them.