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.
He scored against Vaduz in a game that Vojvodina lost 3–1 in the 2011–12 UEFA Europa League qualifying phase.
[3] Subsequently, having spent only a month with Vojvodina, Čović was traded to Spartak Zlatibor Voda.
[6] On 7 April 2023, Čović signed with Chinese Super League club Henan FC, reuniting with former Kunshan manager Sergio Zarco.
[9] Čović got his first call up to the senior Serbia side for the friendly games against Dominican Republic and Panama.