In the youth Musli won the Euroleague Basketball Nike International Junior Tournament twice with FMP dominating in the paint and winning MVP awards, which made him one of the most promising young players of his generation. In January 2009, Musli signed his first professional four-year contract with FMP, team where he spent previous 2 seasons at the junior level. In the summer of 2009, he won with his team the 2009 EuroLeague's NIJT junior tournament, after defeating the Lithuanian Lietuvos rytas. He scored 31 points and grabbed 17 rebounds in the final game, while also guarding Jonas Valančiūnas who scored 22 points. Despite being one of the most promising European players, in March 2010 Musli decided not to enter the 2010 NBA draft.
On September 22, 2010, Musli signed a five-year contract with the Spanish team Caja Laboral. In first season with the team, he saw very little playing time, also having played only two games in his first EuroLeague season. In February 2011, Musli was loaned to the Italian team Montegranaro until the end of season, but was quickly sent back due to concerns about his poor work ethic and questionable attitude. Officially, he didn't play any game for Montegranaro due to illness. In October 2011 he was loaned on one-month assignment to the Spanish side Fuenlabrada, in order to return his game shape. In February 2012, he was once again loaned, this time to Mega Vizura until the end of the season. Over the course of season, he averaged 9.1 points and 6.4 rebounds in the Basketball League of Serbia. He played just ten games over two years in all competitions with Caja Laboral.
Partizan
On 18 July 2012, shortly after terminating his contract with Caja Laboral, Musli signed a three-year contract with Partizan Belgrade, with option to leave after two seasons. In the first EuroLeague season with Partizan, he averaged 9.5 points and 4.9 rebounds over 10 games. After solid first season in Partizan, Musli's minutes per game dropped slightly in his second season with the team, which also reflected on his stats. He averaged 5.3 points and 3.1 rebounds over 23 EuroLeague games. In April 2014, at the Basketball League of Serbia game against Crnokosa, he scored season-high 22 points and added 5 rebounds while spending only 13 minutes on the court. In 2014, he won his second straight and club's 13th consecutive Serbian League defeating Red Star Belgrade with 3-1 in the final series.
On December 30, 2014, Musli signed with Mega Leks for the rest of the season. In a debut for the new team against Cibona, he scored 26 points and grabbed 5 rebounds. Over 10 games in the Adriatic League, he averaged 15 points and 9.2 rebounds per game.
On 9 June 2016, Musli signed a two-year contract with the Spanish club Unicaja. In April 2017, Musli won the EuroCup with Unicaja after beating Valencia BC in the Finals. On December 7, 2017, he parted ways with Unicaja.
