Alexandre Muller was born on February 1, 1997, in Poissy, France, to Stefan and Virginie Muller. His father works for BNP Paribas, while his mother is a mortgage recovery agent. Muller had a tennis court at his home and began playing with his father at the age of 6. He idolized Roger Federer when he was growing up.
The Frenchman competed almost entirely on the ITF Futures Circuit from 2015 until 2018. He reached 19 finals on that Circuit during those years, winning the title in six of them. Five of his title runs came on clay, with the other being on hard court in Cyprus.
Muller eventually began competing on the ATP Challenger Tour. His first Challenger final came in Glasgow, where he lost to Emil Ruusuvuori in the final. A maiden Challenger Tour title came on home soil in Blois in June 2022, beating Nikola Milojevic in the final.
Further Challenger Tour success came in 2023. He was the runner-up to Aleksandar Kovacevic in Waco, Texas, in February. That was followed by his second title in Montechiarugolo, Italy. Both his Challenger titles were on clay. Muller did win one Grand Slam main draw match at the 2021 Australian Open before he made a bigger breakthrough. As a lucky loser, he overcame Juan Ignacio Londero in the opening round, before exiting to Diego Schwartzman.
His breakthrough on the ATP Tour came at the 2023 Marrakech Open. Muller defeated French tennis legend Richard Gasquet, before also beating Francesco Passaro, Lorenzo Musetti, and Pavel Kotov. He came very close to claiming a first title in the final against Roberto Carballes Baena. However, Muler was defeated 6-4, 6-7, 2-6.
After reaching the second round of the 2024 Indian Wells Open, Muller progressed to the Round of 16 at the Italian Open in May of that year. His run included a 3-6, 6-3, 6-2 triumph against the No. 4 seed Andrey Rublev, before being stopped by the eventual runner-up Nicolas Jarry.
