The Golden State Warriors superstar is kick-starting his campaign for Academy Award consideration for his breakout performance as Klay Thompson in "Space Jam 2" ... saying he's trying to add to his trophy case!!!

Now that filming wrapped up ... Klay was joking with the media about launching his official Oscars campaign! It's pretty funny.

“It’s all done ... your boy is going for the Oscar nod,” Thompson joked to NBC Sports Bay Area's "Warriors Outsiders."

“Supporting?! Best animated series!? I don’t know.”

Obviously, Klay ain't got a snowball's chance in hell ... but dude SHOULD be recognized for fighting through the pain of an ACL surgery to be on the set to shoot his scenes.

Remember, Thompson injured himself during the NBA Finals and went under the knife just days before filming started.

But, despite being in serious pain, Klay limped onto the set with crutches to shoot with LeBron James, Anthony Davis, Dame Lillard and more.

Hey, some actors postpone production when they a get a slight cold!!!