Kristoffer Peterson arrived at the Liverpool Academy from Sävedalens IF in January 2011. He made his debut for the Under 18s in the 2010–11 season, however he was to only play the one match for the Under 18s that season as he played more frequently for the Under 16s. During the 2011–12 season, operating mostly as a midfielder, Peterson figured for the Under 18s far more prominently, and produced some eye-catching performances from the centre of the park. He was one of the stand-out performers for the side, netting five goals in 22 games. His good form brought him to the attention of Reserve team coach Rodolfo Borrell, who used the young starlet as a second-half substitute in the Under 19s NextGen Series tie against Molde FK. He also featured in the NextGen Series third place play-off tie against Olympique de Marseille. Now operating further up the pitch, often in a wide forward role, in the 2012–13 season, Peterson continued as one of the U18's star players. He featured 23 times and scored nine goals and also made his step up to the U21s, for whom he featured 13 times- seven of which came in the NextGen Series. Peterson kicked on in the 2013–14 U21s season as he netted all three of Liverpool's goals in their four pre-season friendlies, with goals against Glentoran F.C., Heart of Midlothian F.C. and Bologna F.C. 1909 first teams.
In January 2014 he signed an extension to his contract with Liverpool. and said he would use it to spur him on: "This is the biggest motivation boost in my career. This is the biggest I have ever experienced". He completed the U21s season at Liverpool with 6 goals and 15 appearances to his name. He went on to appear as a substitute in the Liverpool first team's post-season friendly win over Shamrock Rovers at the Aviva Stadium, replacing Iago Aspas in a 4–0 win, being handed the number 54 shirt on 14 May 2014. On 16 July 2014, Peterson came on as a second-half substitute in Liverpool's pre-season match away to Brøndby, and netted a tap-in in the 49th minute after good work from Jordon Ibe. He also scored again in Liverpool's next pre-season match, away at Preston, netting the winner in a 2–1 win. After the game, manager Brendan Rodgers confirmed he would now take Peterson on Liverpool's pre-season tour of America, having initially failed to make the cut, along with the most of the club's younger players.
In January 2017, Peterson joined league rivals Heracles Almelo on a 2.5-year contract with the option a further year.
Swansea City
Peterson signed for Championship club Swansea City on 2 August 2019, reuniting with head coachSteve Cooper, who Peterson had worked with at Liverpool's academy. He made his debut for the club as a substitute in a 2–1 win against Hull City one day later. He scored his first goal for Swansea in an EFL Cup tie against Cambridge United on 28 August 2019.
