On 16 October 2014, it was revealed that Dynamo Moscow are planning to offer to extend Dzsudzsák's contract.
At the time, Dzsudzsák earned €2.6 million, but the club was willing to raise his salary to €3.2 million.
This means that Dzsudzsák would be able to earn 2.7 million HUF/daily.

Although Dzsudzsák scored a goal in the 50th minute against Lokomotiv Moscow in the Moscow derby, Dynamo lost the match 4–2 on 2 November 2014 in the 2014–15 Russian Premier League season.
On the 17th matchday of the Premier League season, Dzsudzsák scored a goal and gave two assists against Amkar Perm at the Arena Khimki.

On 10 December 2014, before the final match of the 2014–15 Europa League group stage match against his former club PSV, Dzsudzsák was honoured by his former club by displaying his footprint at the museum of the club.

On 19 December 2014, Dzsudzsák was awarded the best Hungarian football player of the year 2014 by the journalist of the Hungarian sport journal, nb1.hu.
Dzsudzsák finished first (receiving 111 points), while Roland Juhász (92 points) second and Zoltán Gera third (44 points).

On 23 December 2014, Itasportpress.it revealed that Bundesliga club Borussia Dortmund showed interest in signing Dzsudzsák due to the possible financial problems of the Russian Premier League clubs including Dynamo Moscow.
Previously, Dzsudzsák was linked with Serie A club Lazio and English Premier League clubs, including Liverpool and Everton.

On 15 January 2015, Dzsudzsák was linked again with Lazio.

On 9 April 2015, Dzsudzsák scored a superb goal in the 24th minute against CSKA Moscow in the 2014–15 Russian Premier League season at the Arena Khimki in Moscow.
The Moscow derby ended with a 2–1 victory of Dynamo Moscow.
After the match Dzsudzsák said "we consider this victory as if we had won the final".
On 16 October 2014, it was revealed that Dynamo Moscow are planning to offer to extend Dzsudzsák's contract. At the time, Dzsudzsák earned €2.6 million, but the club was willing to raise his salary to €3.2 million. This means that Dzsudzsák would be able to earn 2.7 million HUF/daily.
Although Dzsudzsák scored a goal in the 50th minute against Lokomotiv Moscow in the Moscow derby, Dynamo lost the match 4–2 on 2 November 2014 in the 2014–15 Russian Premier League season. On the 17th matchday of the Premier League season, Dzsudzsák scored a goal and gave two assists against Amkar Perm at the Arena Khimki.
On 10 December 2014, before the final match of the 2014–15 Europa League group stage match against his former club PSV, Dzsudzsák was honoured by his former club by displaying his footprint at the museum of the club.
On 19 December 2014, Dzsudzsák was awarded the best Hungarian football player of the year 2014 by the journalist of the Hungarian sport journal, nb1.hu. Dzsudzsák finished first (receiving 111 points), while Roland Juhász (92 points) second and Zoltán Gera third (44 points).
On 23 December 2014, Itasportpress.it revealed that Bundesliga club Borussia Dortmund showed interest in signing Dzsudzsák due to the possible financial problems of the Russian Premier League clubs including Dynamo Moscow. Previously, Dzsudzsák was linked with Serie A club Lazio and English Premier League clubs, including Liverpool and Everton.
On 15 January 2015, Dzsudzsák was linked again with Lazio.
On 9 April 2015, Dzsudzsák scored a superb goal in the 24th minute against CSKA Moscow in the 2014–15 Russian Premier League season at the Arena Khimki in Moscow. The Moscow derby ended with a 2–1 victory of Dynamo Moscow. After the match Dzsudzsák said "we consider this victory as if we had won the final".
Balázs Dzsudzsák