*Club domestic league appearances and goals, correct as of 12:00, 18 October 2024 (UTC) ‡ National team caps and goals, correct as of 20:22, 31 January 2022 (UTC)
In the first two seasons of his professional career HNK Rijeka loaned Sluga to Juventus Primavera and Verona Primavera. During the 2013–14 season he was loaned to NK Pomorac in Croatia's Druga HNL where he collected 31 caps and managed 17 clean sheets. He spent the 2014–15 Prva HNL on loan to NK Lokomotiva where he was capped on 26 occasions. He returned to Rijeka following the end of the loan and recorded his official game début on 19 July 2015 against Slaven Belupo. In August 2015, he was loaned to Spezia Calcio in Italy's Serie B.
Luton Town
On 19 July 2019, Sluga joined newly-promoted Championship side Luton Town for a club record fee of €1.5 million, signing a three-year contract.[6] On 2 August 2019, Sluga made his first appearance for Luton in a 3–3 draw against Middlesbrough.[7]