KLAC radio, "the voice of the Los Angeles Lakers and Kings," has offered President Reagan a $100,000-a-year sports talk show slot after he leaves the White House, station officials said Thursday.

In a notarized letter mailed late Wednesday, Norman Epstein, vice president and general manager of KLAC, offered Reagan a one-year contract to serve as sports director and do a one-hour talk show originating from his new home in Bel Air."This is a bonafide offer," said marketing director Robert Novak. "We have a check ready for him. This is not a hoax. We're prepared to build a studio in his home."