VfB Stuttgart beat Norwegian side Viking 3-1 in their opening Champions League fixture of the season on 9 September, with the Bosnian forward scoring all three of his side's goals in a performance that proved a nightmare for Viking's defence.
According to Fussball News, scouts from all four clubs - AC Milan, Juve, Leeds United and Galatasaray - have since intensified their observation of the 28-year-old's performances.
Any club looking to move for Demirović would face a difficult negotiation. The striker is under contract with Stuttgart until June 2028, and the German club are not willing to let him leave for less than €35 million.
Demirović began his career in Spanish football, where he played for Deportivo Alavés and Almería, before Stuttgart signed him in 2024. Since then he has scored 36 goals and provided 11 assists in 92 official matches for the club.
His hat-trick against Viking has only added to a growing reputation built over his two seasons in the Bundesliga, and comes at a time when several of Europe's leading clubs are actively searching for reinforcements up front.
Whether any of Stuttgart's suitors are willing to meet the asking price remains to be seen, but the scale of interest already circling suggests Demirović's stock is unlikely to fall any time soon, particularly if he can continue to deliver performances of this level in continental competition.
Demirović has become an increasingly important figure for Stuttgart since his move from Almería, developing into one of the more reliable goalscorers outside the Bundesliga's traditional elite.
His route through Spanish football, including spells at two clubs who have both fought relegation battles in recent years, makes his rise to attracting interest from Serie A and Süper Lig clubs all the more notable, and underlines the scouting networks that leading European clubs maintain across leagues that might otherwise go unnoticed.