The former Manchester City lynchpin was a stalwart of the Blaugrana team during the 2023-24 season, playing 51 matches with Xavi at the helm.
Gundogan contributed five goals and 14 assists in his debut campaign after leaving Manchester City on a free transfer, but he could walk away from the club for nothing in 12 months' time.
Gundogan only agreed to a two-year contract upon his arrival at Camp Nou, although both parties possess the option to extend his stay by a further season until the summer of 2026.
Whether the Germany international will continue to play a key role under Flick remains to be seen, though, as the ex-Bayern Munich boss is thought to be keen to bring in a new midfielder as a matter of priority.
Gundogan 'to stay at Barcelona amid Turkey links'
Gundogan was recently offered an exit route from Barcelona by Galatasaray president Dursun Ozbek, who claimed that capturing the former Man City lynchpin would be one of his "dreams".
The 33-year-old has Turkish heritage, but according to Mundo Deportivo, Gundogan is currently giving no thought to the possibility of leaving Barcelona this summer.
While the Germany international was disappointed to end the season without a single trophy to his name, he is determined to bring success back to Camp Nou in 2024-25.
As well as being a favourite of Xavi, Gundogan also shares a strong relationship with new boss Flick, who bestowed him with the captain's armband during his short-lived spell with the German national team.
The former Borussia Dortmund man admitted that he felt like he let Flick down after the Barca boss was sacked from his Mannschaft post, and he is determined to repay his internal debt to his compatriot.
Which players could leave Barcelona this summer?
While Gundogan wishes to don the Barcelona colours for a little while longer, La Blaugrana are expected to let several fringe players advance their careers elsewhere, particularly in defence.
Thanks to the emergence of Pau Cubarsi, Ronald Araujo is no longer seen as indispensable, while Marcos Alonso will depart when his contract runs out at the end of the month.
Sergi Roberto's future is also unclear ahead of his own contract expiry, and the future of Frenkie de Jong remains the subject of frequent debate, two years on from Manchester United's relentless pursuit of his signature.
Attacking duo Vitor Roque and Raphinha could be on the move as well, but president Joan Laporta recently insisted that the Blaugrana are under little pressure to make big-money sales, hinting that the likes of Roberto, Jules Kounde and Inigo Martinez could all stay put.