Kosorić played for Slavija Sarajevo from 2004 to 2008. In January 2009, he moved to Serbian SuperLiga club Partizan after being noticed during a friendly game played between Partizan and Slavija in the summer of 2008.[2][3] After not getting many chances there, he moved in January 2010 to another Belgrade club, Rad.
During the winter break of the 2011–12 season, Kosorić moved to Radnički 1923. A year later he would leave Serbia and move to Iraq to join Erbil playing in the Iraqi Premier League. After Iraq, he returned to Serbia and played the second half of the 2013–14 season with Radnički Niš.
In the summer of 2014, Kosorić joined Bosnian Premier League club Željezničar and played for the next two and half years at the Sarajevo based club. While playing at Željezničar, Kosorić became the team captain and received a call for the national team. He left Željezničar in December 2016.[4]
On 30 January 2020, Kosorić came back to Željezničar, signing a two-and-a-half-year contract with the club.[12] On 17 October 2020, in a league win against Olimpik, he made his 100th appearance for Željezničar.[13] In December 2023, Kosorić announced his decision to retire from football.[14] He played his last game for Željezničar against GOŠK Gabela on 16 December.[15]
In January 2024, Kosorić decided to continue his career, joining First League of RS club Romanija Pale.[16]