Sané was born on 11 January 1996 in Essen, Germany and was raised near the Lohrheidestadion, Wattenscheid. He is son of former German rhythmic gymnast, the 1984 Summer Olympics bronze medalist Regina Weber, and former footballer and Senegalese international Souleyman Sané. He was named Leroy in honor of Claude Le Roy, a former head coach of his father. His father met his mother while playing professionally for SG Wattenscheid 09. Souleymane Sané was raised in France; he moved to Germany through his service in the French Army. Sané’s two brothers, Kim and Sidi, have played for the youth side or second XI of major German football clubs.

Sané began playing football in 2001 for the youth team of SG Wattenscheid 09. In 2005, he joined Schalke 04. Three years later, he joined Bayer Leverkusen, before returning to the Schalke youth academy (Nachwuchsleistungszentrum) in 2011.

On 21 March 2014, Sané signed a three-year professional contract with Schalke extending until 30 June 2017. He made his Bundesliga debut on 20 April 2014 against VfB Stuttgart. He replaced Max Meyer after 77 minutes in a 3–1 away defeat. He scored his first goal of the season in a 2–1 home defeat to 1. FC Köln on 13 December. On 11 March 2015, Sané scored in his first UEFA Champions League match in a 4–3 victory over Real Madrid, although his side were knocked out of the competition on 5–4 aggregate.

Sané was first called up to the Germany under-21 team by youth coach Horst Hrubesch on 28 August 2015 for the friendly against Denmark and for the 2017 UEFA European Under-21 Championship qualifier against Azerbaijan. On 3 September 2015, he made his debut for the German U21 side in a 2–1 win at Stadion an der Lohmühle in Lübeck against Denmark, where he was replaced after 73 minutes by Julian Brandt. Sané received his first senior call-up to the German senior team on 6 November 2015 in a friendly against France. On 13 November 2015, he was substituted in the 61st-minute for Julian Draxler in a friendly match against France in Saint-Denis, in what would be a 2–0 defeat for the Germans, overshadowed by shootings and explosions around the stadium.

On 2 August 2016, Sané joined Premier League club Manchester City, signing a five-year contract for a reported £37 million transfer fee, with performance-related add-ons potentially making the fee £46.5 million. He made his debut in a 1–2 win, in the Manchester derby against Manchester United, on 10 September. His first goal for City came in a 2–1 win against Arsenal at home in the Premier League, on 18 December. Following a spell on the sidelines due to injury, Sané made his return in a game against Tottenham Hotspur and scored in a 2–2 draw at the City of Manchester Stadium on 21 January 2017. On 28 January, he scored in a 3–0 away win over Crystal Palace in the FA Cup fourth round match.

In July 2017, Sané said he believed his debut season at City had been limited by his inability to breathe through his nose. He said he particularly suffered during matches, with his constantly blocked nose hampering his performance and causing him intense frustration. He opted to have corrective surgery during the off-season break. Although this caused him to miss that year’s FIFA Confederations Cup, he said his chronic nasal congestion was becoming increasingly unbearable for him and that he wished to enter the next season feeling happy and healthy.

On 9 September 2017, Sané scored his first two goals of the 2017–18 season in City’s 5–0 home win against Liverpool. On 20 September, he scored twice in a 2–1 away win over West Bromwich Albion in the third round match of the League Cup. On 23 September, he scored in a 5–0 win over Crystal Palace. On 14 October, he scored in a 7–2 win over Stoke City. On 21 October, he scored in a 3–0 win over Burnley. On 28 October, he scored in a 3–2 away win over West Bromwich Albion. After scoring and assisting once in each of his three matches, he earned the Premier League Player of the Month award for October 2017. On 6 January 2018, he scored in a 4–1 win in the FA Cup third round over Burnley. On 14 January, he scored in a 4–3 defeat to Liverpool. Nine days later, on 23 January, he scored in a 3–2 away win over Bristol City, securing advancement into the League Cup final, in which he played 77 minutes before being substituted off as City won 3–0 over Arsenal to clinch their first trophy under Pep Guardiola. On 1 March, five days following the win in the final, he scored against Arsenal in a 3–0 league away win. On 31 March, he scored in a 3–1 away win over Everton, putting City just a win away from winning the league title. On 29 April, he scored in a 4–1 away win over West Ham United.

On 15 September 2018, Sané scored the opening goal and his first of the 2018–19 season in City’s 3–0 home win against Fulham. He later scored the final goal in consecutive home match wins over Burnley and Southampton. On 24 November, Sané assisted a first-half goal for Sterling and scored a brace in a 4–0 away win over West Ham United.

Sané was omitted from Germany’s final 23-man squad for the 2018 FIFA World Cup in favour of another young player Julian Brandt on 4 June 2018. In September 2018, after he was selected for the squad to face games against France and Peru, he left the team hotel after a discussion with Joachim Löw, citing “personal reasons” as his cause for leaving. It was later revealed that the reason for leaving was due to the birth of his daughter.

On 16 November 2018 he scored his first goal for Germany against Russia following an assist from Serge Gnabry. The goal came in the eighth minute of the game as Germany won 3–0.

On 3 January 2019, he scored the winning goal for Manchester City in the 72nd minute of the game against Liverpool, which resulted in Liverpool’s first league defeat of the season.

On 21 February 2019, Manchester City were 2–1 down in the first leg of the Champions League round of 16 tie against Sané’s former club, Schalke, playing with only 10 men after Nicolás Otamendi was sent off on the 68th minute. Sané levelled the scores with a stunning free kick from just under 30 yards only seven minutes after being substituted for Sergio Agüero. He chose not to celebrate out of respect for his former club. City went on to win the game 3–2 with the winning goal scored by Raheem Sterling.

On 13 March 2019, in the second leg of the Champions League round of 16 clash against Schalke, Sané put in an incredible performance with three assists and a goal to contribute to Manchester City’s 7–0 victory against his former club, sending City to the quarter-finals of the competition.

On 24 April 2019, Sané scored the second and final goal in a match against Manchester United during the 66th minute to secure City a Manchester derby win. It was his first ever Manchester derby goal.

Sané was repeatedly linked with Bundesliga champions Bayern Munich to replace club staples Franck Ribéry, who was leaving the club, and retiring Arjen Robben. Despite a deal to the German side reportedly being nearly finalized, Sané was surprisingly named in the starting 11 against Liverpool in the FA Community Shield. After only 10 minutes, Sané was substituted after sustaining a torn ACL, ruling him out of competition for the majority of the season and ending talks with Bayern until his injury healed. In June 2020, Sané rejected a contract extension at Manchester City with manager Guardiola stating that he would be leaving the club in the summer.

On 3 July 2020, Bayern Munich agreed to sign a five-year deal with Sané for an initial €45 million with add-ons rising to a potential €60 million.

Sané scored on his Bundesliga debut in an 8–0 win against former club FC Schalke 04. On 3 November 2020, Sané scored his first Champions League goal for Bayern Munich in a 6–2 away win over Red Bull Salzburg in the 2020–21 season.