A "cleat chaser" is a slang term for a girl that chases after baseball players. The pursuit is for no other reason than him being an athlete; the chaser may not even have interest in or knowledge of the sport itself.
Such females would often not even give the player the time of day if he were not an athlete. Cleat chasers range from girls merely wanting to flirt with the athletes or be seen with them to those who are interested in dating the athlete. These girls are also commonly referred to as "groupies" or "jersey chasers."