Born in Sofia, Maleeva is the second oldest of the three children of Georgi Maleev and Yuliya Berberyan. Her mother came from an Armenian family, which found refuge in Bulgaria after the 1896 Armenian massacres in the Ottoman Empire, and was the best Bulgarian tennis player in the 1960s. After she retired from professional tennis in the 1970s, Berberyan started a coaching career. She was the coach of her three daughters, Katerina, Manuela and Magdalena, each of whom eventually became WTA top 10 players.