On 7 January 2014, Hajrović was transferred to Turkish club Galatasaray for a fee of €3.5 million. He made his competitive debut for the club against Bursaspor on 2 February. He scored his first goal for Galatasaray in a cup win over Tokatspor. Three weeks later, Hajrović debuted in UEFA Champions League against Chelsea. Hajrović won his first trophy with the club on 7 May, by beating Eskişehirspor in Turkish Cup final.
On 10 July 2014, Hajrović signed a four-year contract with German team Werder Bremen. On his competitive debut for the team, he opened the scoring against FV Illertissen in DFB-Pokal game. He made his league debut a week later against Hertha BSC. He scored his first league goal on 26 April 2015 against Paderborn 07.
In June 2014, Hajrović was named in Bosnia and Herzegovina's squad for 2014 FIFA World Cup, country's first major competition. He made his competition debut in the opening group match on 15 June, which ended in narrow loss to Argentina at the Maracanã Stadium.
Hajrović married his long-time girlfriend Lejla in May 2014.