Lyon

Kalulu moved from his youth club Saint-Priest to the youth academy of Olympique Lyon in the summer of 2010. In Lyon, he passed through the different youth departments from 2010 to 2018, and was elevated to their reserve team in June 2018. For the home game against Amiens on 5 March 2020, Kalulu was called up for the first team of Lyon, but did not play in the match.^[6]

AC Milan

In the summer of 2020, Kalulu moved to Italy to join AC Milan, and signed a contract until 2025.^[7] On 10 December, he made his professional debut, playing the entire Europa League game against Sparta Prague as a left-sided centre-back; as Milan won 1–0, he was praised for helping the team keep a clean sheet.^[8] Three days later, on 13 December, Kalulu made his debut in Serie A, replacing the injured Matteo Gabbia in the fifth minute of a home game against Parma.^[9] In the following away league game against Genoa played on 16 December, he made his first-ever start in Serie A and scored a debut goal in his senior career, equalizing the score in the eventual 2–2 draw.^[10]

During the 2021–22 season, after an injury to Alessio Romagnoli, Kalulu started the match against Napoli on 6 March 2022, partnering in central defence with Fikayo Tomori; he helped Milan to clinch a 1–0 win, impressing against Napoli's striker Victor Osimhen.^[11] On 12 March against Empoli, Kalulu scored his first goal of the season, a powerful curling shot from outside the box, as Milan managed to win 1–0 and stay top of the league.^[12] With him and Tomori again in central defence, Milan kept clean sheets in two consecutive Serie A games for the first time in 2022.^[13]

In the 2022–23 season, Kalulu played in several different positions all throughout the season such as a right-sided centre-back next to Fikayo Tomori, on the right of a back-three with Malick Thiaw in the middle and Tomori on the left, and as a right full-back in a back-four. However, towards the season's end, as manager Stefano Pioli switched back to 4–2–3–1 formation, Kalulu began to lose his place in the starting XI as a centre-back to Thiaw, the summer signing who emerged in the second half of the season, and team captain Davide Calabria as a right full-back.