[6] In an interview on Budimir's signing, former Croatian international Jurica Vranješ described him as "tall, strong in the air, and reliable in combinations" and compared his style to Dimitar Berbatov.

[9] In June 2016, ahead of Crotone's debut Serie A season, Sampdoria of the same league activated Budimir's release clause believed to be in the region of €1.8 million, and the player signed a deal ending in mid-2020.

[12] He scored his first goal for the Balearic club on 3 February as a Panenka penalty kick in a 2–0 home win over AD Alcorcón, later being sent off.

[18][19] He made his national team debut on 7 October in a friendly 2–1 victory over Switzerland, providing Mario Pašalić with an assist for the winning goal.

[25] Budimir's family comes from the village of Ozimica in Bosnia and Herzegovina, and he was born in Zenica as it was the nearest town with an adequate hospital.