Asanović is a surname. Notable people with the surname include:
Aleksa Asanovic (born 1945), Montenegrin musician Aljoša Asanović (born 1965), Croatian footballer Antonio Asanović (born 1991), Croatian footballer Krste Asanovic, American engineer Sreten Asanović (1931–2016), Montenegrin author Tihomir "Pop" Asanović (born 1948), Croatian keyboardist, Hammond organ player and composer