Donald Sterling -- REJECTED By Law Firms ... He's Radioactive

Donald Sterling has been REJECTED by at least 8 big law firms in his quest to sue the NBA ... we're told because they think he's toxic and would piss off their existing clients.

Multiple sources in the legal world tell TMZ ... Sterling has reached out to a number of extremely large, prestigious firms, both in L.A. and San Francisco, looking for representation ... but none were receptive.

Our sources say partners in the firms feel representing Sterling would alienate both their African American clients and corporate clients that are hyper-sensitive to controversy.

One source closely connected with Sterling tells TMZ ... it's especially galling for the Clippers owner, because a number of partners in these firms have called him from time to time asking for favors, including tickets to games.