A product of the FMP's youth system, Čović spent the first five years of his career playing for their senior side, and a further year and a half playing for Crvena zvezda.
In January 2013, Čović signed for Vojvodina Srbijagas for the remainder of the season.[1] In August 2013, Čović signed for KAOD Dramas of the Greek Basket League,[2] but left the club in December citing personal reasons.[3] Shortly afterwards, he returned to his former club FMP, signing a multi-year contract with them.
In April 2018, Čović signed with Crvena zvezda.[4] On June 25, 2019, Čović signed a two-year extension with Crvena zvezda.[5] In February 2020, he was loaned to FMP for the rest of the 2019–20 season.[6] In his final 2020–21 season, over 23 ABA League games, Čović averaged 11.6 points, 6.7 assists and 2.1 rebounds, while shooting 33.7% from the field.
On 20 May 2021, Čović announced his intentions to retire after the 2021 Serbia League Playoffs.[7] After FMP failed to advance to semifinals Čović retired from professional basketball at age 31.[8]