Richard Richards, the Republican national chairman since January, is apparently on his way out. The only question, according to GOP sources, is when and where. The White House is one possibility, but perhaps not until Richards has spent a year on the job. One rumor has him becoming political affairs chief, but this may be only because that job opened up with the resignation of Lyn Nofziger.

Richards admits he has heard rumors, but says, "I've had no discussions with anyone, or made any plans to move. As far as I know, I'm solid and happy." Quite different reports come from others. Richards' biggest problem: an unfortunate habit of putting his foot in his mouth. One White House strategist described him as a "loose cannon."

Richards, Ronald Reagan's hand-picked choice for the chairmanship, was never a favorite of party moderates. Bill Brock, the former chairman, was their kind of guy. But many New Right leaders feel Richards, a Mormon from Utah, has gone out of his way to alienate them. Their biggest sore point: Richards' attacks on conservative political action groups, which he said "create all kinds of mischief."

Richards also raised eyebrows by saying the GOP has "written off black leaders for criticizing President Reagan's economic policies," and, "It would be a waste of our resources to go out and try to get votes from people who have shut the door on us." His strong suit is his friendly, low-key manner and loyalty to Reagan. "I've enjoyed working with Dick," says one GOP congressional leader. "He never makes a move without checking with the White House."