He made his debut with the Serbian national team in 2012.
Stevanović's parents separated shortly after his birth in Zürich and he never met his biological father. Immediately after the separation, when Alen was only three months old, his mother brought him to Bečmen, SR Serbia to live with his grandmother and uncle while she returned to Switzerland. He could not reach his mother in Zurich as he was not granted a visa and could only see her once a year. His grandfather, who had worked both in Switzerland and had returned to Belgrade, died a year later at the age of 58 years. Until 2004-2005, as stated by himself, he was angry with life and this hindered the beginning of his playing career. He married Dunja on 20 November 2013 and became the father of his first child Neva.
Stevanović started his professional career in Serbia at FK Radnički Obrenovac. In early 2009, a trial was arranged for him at Italian champions Internazionale, and after arriving in Milan on 9 January, Stevanović was signed by the club in February.
In November 2009, Stevanović, along with youngster Giulio Donati, was named to the match-day squad against Livorno in Coppa Italia, but remained an unused sub.
He then traveled with the first team to Abu Dhabi, UAE and Saudi Arabia for winter training camp. He played the friendly match against Saudi Arabian side Al-Hilal as starter.
Due to the injuries incurred by Esteban Cambiasso, Sulley Muntari and Rene Krhin, Stevanović was named in the squad for the first league match after the winter break, against Chievo, but again didn't get any playing time.
A couple of days later, after Patrick Vieira left for Manchester City on 8 January 2010, Stevanović made his Serie A debut the very next day on 9 January at home versus Siena by coming on as a sub for Thiago Motta in the 67th minute. Head coach José Mourinho made the substitution in direct response to Siena taking the 3–2 lead on a goal scored two minutes earlier. By the end, Inter managed to overturn the score 4–3 with an injury time winner.
On 22 July 2010, Stevanović left for Serie B side Torino in co-ownership deal for €2 million., As part of the deal, Inter signed youngster Simone Benedetti in another co-ownership deal also for €2M. He debuted in Coppa Italia against Cosenza, earning a penalty kick. Torino coach Franco Lerda played him a further 8 times throughout the season and once more in Coppa Italia.
On 24 March 2011, it was officially announced that Stevanović would join MLS club Toronto FC on loan. Stevanović made his debut for the club on 26 March 2011 in a 2–0 home victory against Portland Timbers. Following a 1–0 home defeat to Seattle Sounders FC on 18 June in which Stevanović earned his first start in nearly a month, the Serbian attacking midfielder was recalled by Torino.
On 21 June 2011 the co-ownership agreement was renewed for the 2011–12 season. On 4 September 2011, he scored his first goal as professional footballer, giving Torino the lead against Varese. He ended the season with 36 appearances and 3 goals. On 22 June 2012, the co-ownership was once again renewed, with Torino renewing his contract until 30 June 2015. On 26 August 2012, Stevanović has played his first match in 2012–13 season against Siena, playing as a starter. On 30 September 2012, Stevanović has entered in game as a substitute for Mario Santana in 58th minute and score the goal after a cross from Alessio Cerci in 1–5 away league win over Atalanta.
On 19 June 2013, after 15 appearances and 2 goals in Serie A, the co-ownership agreement was resolved in favour of Torino.
On 11 July 2013, he moved to Palermo on loan with the right of redemption for the co-ownership, finalised the next day. He made his debut in the rosanero jersey, during the second round of Coppa Italia won 2-1 against Cremonese, held on 11 August 2013, playing as a starter. On 3 May 2014, after the victory against Novara, 1–0 away, he was promoted to Serie A - with five games to spare. He finished the season with 21 appearances and one in Coppa Italia.
On 24 July 2014 he was loaned to Bari, with the option to redeem his contract. In January 2015 he was recalled by Torino and loaned to Spezia in exchange for the forward Osarimen Ebagua and midfielder Pasquale Schiattarella.
On 31 August 2015, Stevanović joined Partizan from Torino on a free transfer, signing a three-year contract and was given the number 91 shirt. Two days later he was officially presented on the Partizan stadium. On 12 September 2015, Stevanović made his official debut for the club in a Eternal derby against Red Star Belgrade and scored the equalizer for Partizan. On 1 October 2015, Stevanović played his first match for Partizan in UEFA competitions in UEFA Europa League group stage in 1–3 away victory over Augsburg. He scored the leading goal for Partizan against Radnik Surdulica in 2–2 away draw on 14 October 2015. He has played 3 matches in 2015–16 UEFA Europa League group stage.
On 2 March 2016, Stevanović scored a goal in Serbian Cup Quarter final against Radnički Niš in 2–0 home win.
After taking part in two matches for the Serbia U-18 in 2008, on 3 March 2010, he made his debut in the Serbia U-21 team.
On 12 October 2012, he was called up to the senior national team by coach Siniša Mihajlović, making his debut in the 67th minute as a substitute for Zoran Tošić in a defeat against Belgium in 2014 FIFA World Cup qualifier. On 22 March 2013, Stevanović was the first time in the starting lineup in the Serbian national team in his career against the Croatia on Maksimir.As of 23 May 2015
As of 18 December 2013
Serie B: 2013–14
Serbian SuperLiga: 2016–17
Serbian Cup: 2015–16, 2016–17