Born in Podgorica, he raised through the ranks of Budućnost where he made his senior debut playing in the Montenegrin First League in the 2012–13 season.
In the first leg played on 14 July 2016, Raspopović was a starter, although Budućnost lost by a score of 2–0 at Genk's Luminus Arena.
[2] It was arguably Raspopović's first encounter with a team from a significantly stronger league, as Genk at the time fielded the likes of Wilfred Ndidi.
[3][4] Raspopović was loaned to Rijeka in January 2018, after which he made his league debut in a 4–0 victory against NK Istra 1961 on 10 February 2018.
[5] After playing a total of eight league games for the rest of the 2017–18 season, Rijeka opted to buy Raspopović's contract from Budućnost, after which he was no a loaned player.