Čović came through the Vojvodina youth categories, and began his professional career at the age of 16 at Cement Beočin, making 19 league appearances and scoring 5 goals.[1] He said: "The goal was to continue the tradition, since all the men from my closest family started their careers in Cement. It is interesting that all of them were defenders, I am the only forward".[2]
On 7 April 2023, Čović signed with Chinese Super League club Henan, reuniting with former Kunshan manager Sergio Zarco.[7] He scored 15 goals in his first season in the top division, surpassing Leandro Netto's record in 2011 (14 goals) of most goals scored by a Henan player in a Chinese Super League season.[8]
Čović got his first call up to the senior Serbia side for the friendly games against Dominican Republic and Panama.[10] He made his debut on 25 January 2021, as a substitution during halftime.[11] In the second half of a draw game against Panama he took captain's armband.[12]