NBA's Damian Lillard -- Rap Career BOOMIN' ... Major Labels Interested

There's a war over Damian Lillard ... with several "major" record labels vying to sign the NBA star to a serious rap deal, this according to his agent.

Lillard's already established himself as one of the best (if not THE best) rapper in the NBA -- and famously started the 4-bar Friday freestyle rap challenge on social media.

He's also racked up more than 4.5 million plays on his SoundCloud page.

Now, the record labels want a piece of the action -- with his agent, Aaron Goodwin, telling TMZ Sports they've been approached by "several major labels" ... though he wouldn't specify which ones.

Goodwin says Lillard is interested -- but doesn't want go down that road until after the NBA season is over.

"We've put it on hold until the summer," Goodwin says ... "We will explore those options versus starting his own label. A distribution partner is really what's needed."

Meantime, Dame Dolla is still droppin' new tracks -- including his new single "Talk To 'Em" which already has more than 40,000 plays. Not bad ...