Alexander "Sascha" Zverev was born on 20 April 1997 in Hamburg, Germany, to Irina Zvereva and Alexander Mikhailovich Zverev. He has an older brother Mischa who was born nearly a decade earlier and is a professional tennis player as well. Both of Sascha's parents were professional tennis players for the Soviet Union. His father was ranked as high as No. 175 in the world. He was also the top-ranked men's player nationally, while his mother was the fourth-highest ranked women's player. They both moved from Sochi to the capital to train at the CSKA Moscow military-run tennis club. The Soviet government often restricted their players from competing outside the country, an impediment that limited how high either of Sascha's parents could rise in the world rankings. With the collapse of the Soviet Union imminent, Irina went to Germany to compete at a tournament in 1990, with her husband accompanying as her coach. While in Germany, they were offered jobs as tennis instructors. After initially declining, they accepted an offer to work at the Uhlenhorster Hockey Club in Hamburg the following year and ended up settling in the country.