Early career and Espanyol Maxim started his football career with local side Olimpia Piatra Neamț when he was seven years old before joining Ardealul Cluj in 2004, sharing teams at some point with
Mihai Răduț and
Vlad Chiricheș. Aged 17, Maxim moved to Spain with
Espanyol. About his accommodation in the country, he said that "it was not very easy". After progressing through the club's academy, he then played for the
reserves in the
Segunda División B.
Pandurii Târgu Jiu On 9 August 2011, Maxim returned to Romania to sign a one-year contract with the option of another two years for
Pandurii Târgu Jiu. Maxim made his debut in the
Liga I on 12 September 2011, coming on as a late substitute in a 5–1 win over
Mioveni, and scored his first goal for the club on 18 December in a 1–1 draw with
Ceahlăul Piatra Neamț. He netted his second on 31 March 2012, in a 1–1 draw against
Steaua București. Maxim later scored two more goals against
Oțelul Galați and
Concordia Chiajna respectively. Despite being absent on some occasions, Maxim finished his first season at the club with four goals in 28 appearances all competitions comprised. The
following campaign, Maxim aided Pandurii to a perfect start after scoring one each against Ceahlăul Piatra Neamț and Oțelul Galați, with the team having managed six wins in the first seven matches. By the time the first half of the season came to an end, he had played 20 games and scored three more goals. Maxim's good display attracted interest from several foreign clubs, including
Standard Liège, and Steaua București was close to reaching an agreement for his transfer. In response to the initial rumours, head coach
Petre Grigoraș stated that he expects the player to stay at Pandurii until the summer of the next year.
VfB Stuttgart , on 28 August 2013 On 31 January 2013, Maxim joined German side
VfB Stuttgart for a transfer fee of
€1.5 million, signing a four-and-a-half-year contract. Maxim made his debut for Stuttgart on 14 February 2013, in a
UEFA Europa League round of 32 game against
Genk. On 23 February, he played his first
Bundesliga match against
Nürnberg. On 30 March, Maxim scored his first goal against defending champions
Borussia Dortmund, to equalise in an eventual 2–1 loss due to
Robert Lewandowski's late goal. Despite suffering an injury, Maxim made fourteen appearances in all competitions and played 62 minutes before being substituted in the
final of the
2012–13 DFB-Pokal, which saw Stuttgart lose 3–2 to
Bayern Munich. On 1 September 2013, Maxim scored his first double for the club while also offering two assists in the 6–2 thrashing of
Hoffenheim, to give Stuttgart the first Bundesliga win of the season after four match-days. He continued with his good form by scoring an assist in the next Bundesliga match against
Hertha BSC in their 1–0 away victory. Maxim then scored again on 29 September 2013, in a 4–0 win over
Eintracht Braunschweig and scored two weeks later on 20 October 2013, in a 3–3 draw against
Hamburger SV. Coincidentally, Maxim scored twice against them for the second time this season on 8 March 2014 and two weeks later on 22 March 2014. He scored 9 goals in 26 matches in the
2013–14 Bundesliga, also contributing 11 assists. In the 2014–15 season, Maxim started the season well when he scored the club's first goal of the season, in a 1–1 draw against
Borussia Mönchengladbach. However, Maxim suffered an injury that kept him out for a week and after making his return, where he came on as a substitute in the second half, in a 3–3 draw against
Bayer Leverkusen, Maxim played the role in the next game, where he set up two goals, in a 5–4 win over
Eintracht Frankfurt on 25 October 2014 and then in the second time meeting on 21 March 2015, he scored and set up one of the goals, in a 3–1 win. Despite suffering from another injury, Maxim made twenty–six appearances and scored two times, as well as, assisting six times in the 2014–15 season. Ahead of the 2015–16 season, it was announced on 11 August 2015 that Maxim extended his contract with VfB Stuttgart until June 2019. The following month on 23 September 2015, Maxim scored his first goal of the season, in a 3–1 win over
Hannover 96 and then scored his second goal of the season on 28 October 2015, in the second round of
DFB-Pokal, in a 2–0 win over
Carl Zeiss Jena. After suffering from an illness that kept him out for a week, Maxim set up two goals on 2 May 2016, in a 6–2 loss against
Werder Bremen. While the club was relegated to the
2. Bundesliga, Maxim scored once in 25 league appearances and assisting six times in the 2015–16 season. Following the club's relegation to 2. Bundesliga, Maxim was given a number 10 shirt from the previous 44 shirt and started the 2016–17 season well when he scored in the opening game of the season, with a 2–1 win over
St. Pauli. On 30 October 2016, he scored again, in a 3–1 win over
Karlsruher SC. After suffering from an injury for one game, Maxim then made his return from injury on 12 December 2016, where he came on as a substitute in the second half, in a 2–2 draw against
Hannover 96. He finished strongly appearing as a regular starter and contributing three goals and one assist in the last matches of the season which helped secure Stuttgart's promotion to the Bundesliga. In his four and a half years at the club, Maxim amassed 131 appearances with 17 goals and 35 assists across all competitions. On 14 October 2017, Maxim scored his first goal for Mainz in a 3–2 league victory over
Hamburger SV. ==International career==