Romeo: We Want Dame Lillard ... ON NO LIMIT FOREVER

Romeo Miller is trying to put an end to Dame Lillard's search for a major rap label ... by publicly offering the NBA star a record deal on his and his dad, Master P's, record label, No Limit Forever.

We broke the story ... Lillard's being heavily courted (see what we did there) by huge rap labels looking to turn his heavily praised rhyming skills into some moola ... and Dame is weighing his options.

Enter Romeo -- president of No Limit Forever Records -- who told us he's more than willing to give Dame a deal ... and maybe even let him be his own boss.