Career
Early career
Maksimović began his career in 2002 with Kosmos Bajina Bašta, for which he represented in the various youth competitions in Serbia, before he moved to FK Sloga Bajina Bašta in 2004. On 16 July 2006 he moved to the youth ranks of Sloboda Užice, where, precisely two years later, he made his debut for the first team in a game against FBK Kaunas. On 19 September 2010 Maksimović received the first yellow card of his career during a match against Spartak Subotica.
And scored the first goal of his professional career on 5 March 2011 in Lučani.
Red Star
During the 2012 winter transfer window Maksimović was signed by Serbian giants Red Star Belgrade, for a reported fee of €300,000. He made his debut on 3 March 2012 in a match against Spartak Zlatibor.
At the end of the season 51% of his contract was acquired by Cypriots Apollon Limassol. Torino
On 23 July 2013 he was loaned to Italian Serie A club Torino with a buyout clause.
He made his official debut on 6 October as a substitute against Sampdoria in Genoa, finishing 2–2.
Over the course of the season he earned a spot in the starting lineup, first, as a central defender, then as a right-sided midfielder. On 27 May 2014 Torino exercised the right to purchase him outright. Maksimović signed a contract until 2018.
He made 4 appearances for the Serbian national youth teams: two with the under-19 and two with the under-21.
He was first called up to the Serbian national team on 31 May 2012, for two friendly matches against France and Sweden, in which he was played as a starter. Able to play as a defensive midfielder, he grew up playing mainly as a central defender.
He is agile for his considerable height (193 cm), combined with a predisposition for the air and marking opponents. At home he has been repeatedly compared to Nemanja Vidić.