Overseers of the Kentucky athletics program have ordered basketball Coach Joe B. Hall and Athletic Director Cliff Hagan to negotiate terms of a game with Louisville.

Louisville and Kentucky have met only five times--each time in postseason play--since the last regularly scheduled game, in 1922. In the NCAA Mideast Regional final last month, Louisville defeated Kentucky, 80-68 . . .

The South Carolina board of trustees voted unanimously to accept an invitation to join the Metro Conference. The move ends 12 years of independent status for the Gamecocks, who dropped out of the Atlantic Coast Conference in 1971 . . .

Two names were inadvertently left off The Washington Post's list, printed Sunday, of area Division I basketball players. De Matha's Pat Smith was a freshman reserve guard for Harvard last year and McNamara's Todd Bozeman was a sophomore swing man for Rhode Island . . .

An Associated Press item reported in The Post yesterday was inaccurate. The story said that 95 percent of the athletes at Iowa State scored at below 10th-grade level on reading tests and that 10 percent were functionally illiterate, or scored below fourth-grade level.

The tests were actually limited to a group of 28 incoming basketball and football players. Dr. Gerald Gurney, the academic counselor for the ISU athletic department, said the tests showed that 27 of the 28 players read at or below 10th-grade level and that three were functionally illiterate.

The original story also reported on a Virginia Tech faculty study that showed that athletes at the school have much lower grades and a lower graduation rate than the general student body.

Of 164 athletes enrolled at VPI last fall who had attended the school for at least one term, 41 percent had grade-point averages below 2.0 on a 4-point scale, according to the study released in Blacksburg . . .

Washington will have a chance to salute Coach Jim Valvano and the D.C. Three of North Carolina State's championship basketball team that was balked by the NCAA from accepting President Reagan's invitation to the White House. Set Wednesday, May 4, at the Touchdown Club is a Washington Basketball Hall of Fame salute--and "no problem with NCAA regulations," says the hall's director, Bob Geoghan. The Wolfpack's Thurl Bailey, Dereck Whittenburg and Sidney Lowe will be up on a legitimate visit home. Tickets are $15, via the TD Club . . .

At William and Mary, assistant basketball coach Barry Parkhill stepped up to head coach, replacing his brother Bruce, now at Penn State.