Youth and college Mueller grew up in
Schaumburg, Illinois and played
college soccer at the
University of Wisconsin from 2014 to 2017, scoring 22 goals in 75 regular season matches. In 2016, Mueller was selected to the All-America third-team and the All-Big Ten first team. In 2017, Mueller was named
Big Ten Offensive Player of the Year, as well as being selected to the All-Big Ten first team and the All-America second-team.
Orlando City Mueller was drafted as the sixth overall pick of the
2018 MLS SuperDraft by
Orlando City SC. He made his professional debut on March 3, 2018, in a season-opening 1–1 draw with
D.C. United. On April 8, 2018, Mueller scored his first professional goal against
Portland Timbers in a 3–2 victory. On April 21, 2018, Mueller scored the fastest goal in Orlando City history when he scored 63 seconds into a match against the
San Jose Earthquakes, and later in the match he recorded his first professional assist. Mueller was runner-up for the 2018
MLS Rookie of the Year Award. On March 2, 2019, Mueller started in his second consecutive season opener, scoring in a 2–2 against
New York City FC. He scored his first
U.S. Open Cup goal against the same opposition on July 10, 2019, in a 1–1 quarter-final draw before Orlando progressed to their first ever semi-final on
penalties. In July 2019, Mueller was part of the Orlando City team alongside
Nani and
Sebas Méndez that won the
2019 MLS All-Star Skills Challenge, beating teams from the
MLS All-Stars and
Atlético Madrid to win the $25,000 prize for charity with Mueller notably the only player to successfully complete a
scissors kick during the volleys round. On March 7, 2020, Mueller scored Orlando's first goal of the season in a 2–1 away loss to
Colorado Rapids. With the season affected by the coronavirus pandemic, a return to play was achieved through the
MLS is Back Tournament. Mueller scored in the opening game as Orlando beat newly formed rivals
Inter Miami CF 2–1 before scoring a brace in the following game, a 3–1 victory over
New York City FC. He finished the
2020 season as the team's top scorer with a career-high 10 goals. On July 17, 2021, Mueller appeared as a substitute in 1–1 draw with
Toronto FC. It was his 108th appearance for the club in all competitions, tying the record set by
Cristian Higuita in 2019. Entering the final year of his contract in 2021, Mueller had been in contract negotiations with Orlando City but informed the club on July 21, 2021, that he had signed a
pre-contract agreement with an unnamed European club and that he would be leaving upon the expiry of his contract at the end of the
2021 season. He broke the club appearance record a day later, starting in a 2–1 win over
Philadelphia Union.
Hibernian On July 22, 2021,
Scottish Premiership side
Hibernian announced they had signed Mueller on a free transfer agreement, which would see him join the club on January 1, 2022. On January 20, 2022, Mueller made his debut for
Hibernian in the side's 1–0 win over
Cove Rangers in the
Scottish Cup. On February 13, 2022, He scored his first goal for the club in a 3–1 win over
Arbroath F.C. in the Scottish Cup. This proved to be the only goal Mueller would score for Hibs, and he was allowed to return to the U.S. in May 2022. Hibs chief executive Ben Kensell said that Mueller had struggled to "adapt to the pace and physicality" of Scottish soccer. ==International career==