Joe Rogan talked with cops after Liver King challenged him to a fight via social media … and Joe told police the fitness influencer appeared to be “significantly unstable.”

According to new legal docs, obtained by TMZ, cops in Austin, Texas say the former “Fear Factor” host told them he interpreted Liver King’s string of social media rants as threatening … which is why cops were called and eventually led to LK being arrested on a charge of making a terroristic threat.

Police say Joe told them he’d never had any sort of contact with Liver King — real name Brian Johnson — and was unaware why he’d “be targeting him” … and cops say Rogan went on to tell them he’d been told Liver King “has a significant drug issue.”

As we reported … cops say Liver King traveled from Willis, Texas to Austin, where Joe lives and records his famous Spotify podcast, and they busted him at a hotel Tuesday night after he kept ranting online about wanting to fight Rogan.

IYDK … Liver King achieved fame as a fitness influencer who sold health supplements based on a primitive lifestyle he showcased online, though he later admitted steroids and human growth hormone were actually the reason for his muscular build.