Maxim recorded his professional debut for the reserve team of Espanyol in 2009, and also had a loan spell at Badalona before returning to Romania with Pandurii Târgu Jiu in 2011.

His display prompted a move to Germany at the start of 2013, where he amassed Bundesliga totals of 140 games and 14 goals representing VfB Stuttgart and Mainz 05.

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.

[9] 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,[10] and scored his first goal for the club on 18 December in a 1–1 draw with Ceahlăul Piatra Neamț.

The following campaign, Maxim aided Pandurii to a perfect start after scoring one each against Ceahlăul Piatra Neamț and Oțelul Galați,[17][18] with the team having managed six wins in the first seven matches.

[19][20][21] Maxim's good display attracted interest from several foreign clubs,[22][23] including Standard Liège,[24] and Steaua București was close to reaching an agreement for his transfer.

[25][26] 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.

[27][28] 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.

[33] Despite suffering an injury,[34] 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.

[35] 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.

[55] 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.

[66] Two months later on 14 November 2012, Maxim scored again in a 2–1 victory against Belgium,[67] but the match was later deemed unofficial according to the Laws of the Game (excessive number of substitutions).