Glouchkov began playing with Bulgaria's national team as a teenager. After one successful season with the Luskov Yambol junior side, he got promoted to their senior side by his junior coach Simeon Varchev. They also worked together in BC Balkan Botevgrad and Akademik Varna. By the mid-1980s, he had established a reputation as one of Europe's top five players. After averaging 23 points and 19 rebounds during the 1984-85 season in which his team Akademik Varna won the national championship, he attracted the attention of the Phoenix Suns, who selected him in the seventh round (148th pick overall) of the 1985 NBA Draft. The Suns signed him to much fanfare on September 25, 1985, releasing a special press kit which included a history of Bulgaria and a glossary of Bulgarian phrases.