The Game met with the LAPD moments ago over Tuesday's street fight outside a Hollywood nightclub -- and law enforcement sources tell TMZ, the rapper will NOT be arrested.

Game voluntarily rolled down to the Hollywood Police Station this afternoon (video above) -- joking with us that his cat was stuck in a tree -- but the rapper was there for serious business.

We're told ... Game defended his position over the incident outside Colony nightclub -- that he hit no one -- and after interviewing witnesses and reviewing fight footage, cops bought Game's story.