Kleine, a seven-foot center, graduated from Slater High School in Slater, Missouri and originally enrolled to play basketball at the University of Notre Dame. After his freshman season, Kleine transferred to the University of Arkansas. Kleine was selected by the Sacramento Kings with the sixth pick in the 1985 NBA Draft. He went on to have a fifteen-year NBA career, playing with the Kings as well as the Boston Celtics, Phoenix Suns, Los Angeles Lakers, New Jersey Nets, Chicago Bulls, and Portland Trail Blazers. He won an NBA championship ring in 1998 as a reserve center for the Bulls. His best season was with the Kings in 1985, when he averaged 9.8 PPG. At the time of his retirement from the NBA, he’d scored 4,666 points, had 3,991 total rebounds, and had scored 849 free throws out of 1,069 attempts.

Kleine played for the US national team in the 1982 FIBA World Championship, winning the silver medal. Along with his college teammate Robertson, he also won a gold medal as a member of the 1984 U.S. Olympic basketball team coached by Bob Knight. After coaching AAU and high school basketball in Little Rock and serving as an analyst for Arkansas basketball games, he was hired as an assistant coach at the University of Arkansas at Little Rock in 2007.