[9] On 31 August 2016, the last day of summer transfer window, Radošević signed for Austrian giants Red Bull Salzburg as a free agent.

[15] In the following season, after Niels Frederiksen took over as head coach of Brøndby, Radošević continued as a starter on defensive midfield before suffering a shoulder injury in a 5–2 win over Randers FC on 27 October 2019.

[19] This meant that he missed games against rivals Copenhagen and the UEFA Champions League first play-off tie against his former team Red Bull Salzburg.

[22] On 3 September 2023, Radošević played his 147th Superliga game for Brøndby, surpassing Johan Larsson as the non-Dane with the most league appearances for the club.

Radošević was a part of the Croatian national under-17 team in the qualifications for the 2011 UEFA European Under-17 Football Championship, playing in all six group games.

In August 2012, Radošević was called up to the national team by manager Igor Štimac for the 2014 FIFA World Cup qualification matches against Macedonia and Belgium as an alternative for the defensive midfielder Ognjen Vukojević.