Photos surfaced today showing Game and Khloe -- who's married to Lamar Odom -- hugging it out in L.A.'s Runyon Canyon Park last month ... where Game's been doing a "60 Days of Fitness" program.
You'll recall, Khloe's brother Rob Kardashian is also doing the program ... and Game tells us, Khloe is too, which is why they were hanging out.
The Game says, "The pictures that they see of us out together are because she is a part of my 60DaysofFitness team."
The Game adds, "Khloe is my friend. She is like a sister. We have never and will never be sleeping together. Lamar is my homie and her husband and I wish people wouldn’t spread such false rumors."