Watford was thrashed 6-0 at Wembley as City became the first English men's team to complete a clean sweep, adding the FA Cup to its Premier League and EFL Cup titles.
Gundogan is heading into the final year of his contract at the club, which also won the Community Shield at the start of the season.
The Germany international has enjoyed extra responsibility under Pep Guardiola this season, making 31 Premier League appearances, partly down to injury issues for Fernandinho and Kevin De Bruyne.
City has already lost Vincent Kompany after the club captain left to take a player-manager role at Anderlecht but Gundogan suggested he will stay at the Etihad Stadium.
"Now is enough time to reflect on the situation and to take up the talks again more intensely with the club," he told Bild of his contract situation.
While City made history domestically, Guardiola has acknowledged his time at the club will be judged by European success.
And his side fell short again in its bid for a Champions League crown as it was knocked out by Premier League rival Tottenham in stunning fashion.
"The exit in Europe was extremely bitter," Gundogan said of the quarter-final defeat. "But it would be wrong to mourn the Champions League after our domestic success.
"If I can wish for something at club level for my future, then it is definitely to win the Champions League.”